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Functions/Complex

This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.

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Filename: Functions/Complex
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File contents
%OP%VS4.12 Test (Dec 12 1991), Colton Software - Development, R0123 4567 8901 2345
%OP%DP4
%OP%LP*
%OP%TM4
%OP%BM4
%OP%LM5
%OP%FX
%OP%FY
%OP%FS
%OP%WC216,1492,460,1200,0,0,0,0
%CO:A,12,100%
%C%%H1%Complex Functions Examples

%C%Function

 z
w
z+w
z-w
z*w
z/w
z^w
exp(z)
ln(z)
cos(z)
sin(z)
tan(z)
acos(z)
asin(z)
atan(z)
cosh(z)
sinh(z)
tanh(z)
acosh(z)
asinh(z)
atanh(z)
cosec(z)
cot(z)
sec(z)
acosec(z)
acot(z)
asec(z)
cosech(z)
coth(z)
sech(z)
acosech(z)
acoth(z)
asech(z)
%CO:B,10,0%


%R%Real

%V%%R%1
%V%%R%2
%V%%R%index(c_add({$B$6,$C$6},{$B$7,$C$7}),1,1)
%V%%R%index(c_sub({$B$6,$C$6},{$B$7,$C$7}),1,1)
%V%%R%index(c_mul({$B$6,$C$6},{$B$7,$C$7}),1,1)
%V%%R%index(c_div({$B$6,$C$6},{$B$7,$C$7}),1,1)
%V%%R%index(c_power({$B$6,$C$6},{$B$7,$C$7}),1,1)
%V%%R%index(c_exp({$B$6,$C$6}),1,1)
%V%%R%index(c_ln({$B$6,$C$6}),1,1)
%V%%R%index(c_cos({$B$6,$C$6}),1,1)
%V%%R%index(c_sin({$B$6,$C$6}),1,1)
%V%%R%index(c_tan({$B$6,$C$6}),1,1)
%V%%R%index(c_acos({$B$6,$C$6}),1,1)
%V%%R%index(c_asin({$B$6,$C$6}),1,1)
%V%%R%index(c_atan({$B$6,$C$6}),1,1)
%V%%R%index(c_cosh({$B$6,$C$6}),1,1)
%V%%R%index(c_sinh({$B$6,$C$6}),1,1)
%V%%R%index(c_tanh({$B$6,$C$6}),1,1)
%V%%R%index(c_acosh({$B$6,$C$6}),1,1)
%V%%R%index(c_asinh({$B$6,$C$6}),1,1)
%V%%R%index(c_atanh({$B$6,$C$6}),1,1)
%V%%R%index(c_cosec({$B$6,$C$6}),1,1)
%V%%R%index(c_cot({$B$6,$C$6}),1,1)
%V%%R%index(c_sec({$B$6,$C$6}),1,1)
%V%%R%index(c_acosec({$B$6,$C$6}),1,1)
%V%%R%index(c_acot({$B$6,$C$6}),1,1)
%V%%R%index(c_asec({$B$6,$C$6}),1,1)
%V%%R%index(c_cosech({$B$6,$C$6}),1,1)
%V%%R%index(c_coth({$B$6,$C$6}),1,1)
%V%%R%index(c_sech({$B$6,$C$6}),1,1)
%V%%R%index(c_acosech({$B$6,$C$6}),1,1)
%V%%R%index(c_acoth({$B$6,$C$6}),1,1)
%V%%R%index(c_asech({$B$6,$C$6}),1,1)
%CO:C,10,0%


%R%Imaginary

%V%%R%1
%V%%R%-1
%V%%R%index(c_add({$B$6,$C$6},{$B$7,$C$7}),2,1)
%V%%R%index(c_sub({$B$6,$C$6},{$B$7,$C$7}),2,1)
%V%%R%index(c_mul({$B$6,$C$6},{$B$7,$C$7}),2,1)
%V%%R%index(c_div({$B$6,$C$6},{$B$7,$C$7}),2,1)
%V%%R%index(c_power({$B$6,$C$6},{$B$7,$C$7}),2,1)
%V%%R%index(c_exp({$B$6,$C$6}),2,1)
%V%%R%index(c_ln({$B$6,$C$6}),2,1)
%V%%R%index(c_cos({$B$6,$C$6}),2,1)
%V%%R%index(c_sin({$B$6,$C$6}),2,1)
%V%%R%index(c_tan({$B$6,$C$6}),2,1)
%V%%R%index(c_acos({$B$6,$C$6}),2,1)
%V%%R%index(c_atan({$B$6,$C$6}),2,1)
%V%%R%index(c_atan({$B$6,$C$6}),2,1)
%V%%R%index(c_cosh({$B$6,$C$6}),2,1)
%V%%R%index(c_sinh({$B$6,$C$6}),2,1)
%V%%R%index(c_tanh({$B$6,$C$6}),2,1)
%V%%R%index(c_acosh({$B$6,$C$6}),2,1)
%V%%R%index(c_asinh({$B$6,$C$6}),2,1)
%V%%R%index(c_atanh({$B$6,$C$6}),2,1)
%V%%R%index(c_cosec({$B$6,$C$6}),2,1)
%V%%R%index(c_cot({$B$6,$C$6}),2,1)
%V%%R%index(c_sec({$B$6,$C$6}),2,1)
%V%%R%index(c_acosec({$B$6,$C$6}),2,1)
%V%%R%index(c_acot({$B$6,$C$6}),2,1)
%V%%R%index(c_asec({$B$6,$C$6}),2,1)
%V%%R%index(c_cosech({$B$6,$C$6}),2,1)
%V%%R%index(c_coth({$B$6,$C$6}),2,1)
%V%%R%index(c_sech({$B$6,$C$6}),2,1)
%V%%R%index(c_acosech({$B$6,$C$6}),2,1)
%V%%R%index(c_acoth({$B$6,$C$6}),2,1)
%V%%R%index(c_asech({$B$6,$C$6}),2,1)
%CO:D,10,0%


%R%Modulus

%V%%R%c_radius({B6,C6})
%V%%R%c_radius({B7,C7})
%V%%R%c_radius({B8,C8})
%V%%R%c_radius({B9,C9})
%V%%R%c_radius({B10,C10})
%V%%R%c_radius({B11,C11})
%V%%R%c_radius({B12,C12})
%V%%R%c_radius({B13,C13})
%V%%R%c_radius({B14,C14})
%V%%R%c_radius({B15,C15})
%V%%R%c_radius({B16,C16})
%V%%R%c_radius({B17,C17})
%V%%R%c_radius({B18,C18})
%V%%R%c_radius({B19,C19})
%V%%R%c_radius({B20,C20})
%V%%R%c_radius({B21,C21})
%V%%R%c_radius({B22,C22})
%V%%R%c_radius({B23,C23})
%V%%R%c_radius({B24,C24})
%V%%R%c_radius({B25,C25})
%V%%R%c_radius({B26,C26})
%V%%R%c_radius({B27,C27})
%V%%R%c_radius({B28,C28})
%V%%R%c_radius({B29,C29})
%V%%R%c_radius({B30,C30})
%V%%R%c_radius({B31,C31})
%V%%R%c_radius({B32,C32})
%V%%R%c_radius({B33,C33})
%V%%R%c_radius({B34,C34})
%V%%R%c_radius({B35,C35})
%V%%R%c_radius({B36,C36})
%V%%R%c_radius({B37,C37})
%V%%R%c_radius({B38,C38})
%CO:E,10,0%


%R%Argument

%V%%R%c_theta({B6,C6})
%V%%R%c_theta({B7,C7})
%V%%R%c_theta({B8,C8})
%V%%R%c_theta({B9,C9})
%V%%R%c_theta({B10,C10})
%V%%R%c_theta({B11,C11})
%V%%R%c_theta({B12,C12})
%V%%R%c_theta({B13,C13})
%V%%R%c_theta({B14,C14})
%V%%R%c_theta({B15,C15})
%V%%R%c_theta({B16,C16})
%V%%R%c_theta({B17,C17})
%V%%R%c_theta({B18,C18})
%V%%R%c_theta({B19,C19})
%V%%R%c_theta({B20,C20})
%V%%R%c_theta({B21,C21})
%V%%R%c_theta({B22,C22})
%V%%R%c_theta({B23,C23})
%V%%R%c_theta({B24,C24})
%V%%R%c_theta({B25,C25})
%V%%R%c_theta({B26,C26})
%V%%R%c_theta({B27,C27})
%V%%R%c_theta({B28,C28})
%V%%R%c_theta({B29,C29})
%V%%R%c_theta({B30,C30})
%V%%R%c_theta({B31,C31})
%V%%R%c_theta({B32,C32})
%V%%R%c_theta({B33,C33})
%V%%R%c_theta({B34,C34})
%V%%R%c_theta({B35,C35})
%V%%R%c_theta({B36,C36})
%V%%R%c_theta({B37,C37})
%V%%R%c_theta({B38,C38})
%CO:F,1,0%%CO:G,49,56%


Summary

Defining complex number z.
Defining complex number w.
Adds two complex numbers.
Subtracts two complex numbers.
Multiplies two complex numbers.
Divides one complex number by another.
Raises one complex number to the power of another.
Raises e (natural exponent) to the power of a complex number.
Returns the natural logarithm of a complex number.
Returns the Cosine of a complex number.
Returns the Sine of a complex number.
Returns the Tangent of a complex number.
Returns the inverse Cosine of a complex number.
Returns the inverse Sine of a complex number.
Returns the inverse Tangent of a complex number.
Returns the hyperbolic Cosine of a complex number.
Returns the hyperbolic Sine of a complex number.
Returns the hyperbolic Tangent of a complex number.
Returns the inverse hyperbolic Cosine of a complex number.
Returns the inverse hyperbolic Sine of a complex number.
Returns the inverse hyperbolic Tangent of a complex number.
Returns the Cosecant of a complex number.
Returns the Cotangent of a complex number.
Returns the Secant of a complex number.
Returns the inverse Cosecant of a complex number.
Returns the inverse Cotangent of a complex number.
Returns the inverse Secant of a complex number.
Returns the hyperbolic Cosecant of a complex number.
Returns the hyperbolic Cotangent of a complex number.
Returns the hyperbolic Secant of a complex number.
Returns the inverse hyperbolic Cosecant of a complex number.
Returns the inverse hyperbolic Cotangent of a complex number.
Returns the inverse hyperbolic Secant of a complex number.
00000000  25 4f 50 25 56 53 34 2e  31 32 20 54 65 73 74 20  |%OP%VS4.12 Test |
00000010  28 44 65 63 20 31 32 20  31 39 39 31 29 2c 20 43  |(Dec 12 1991), C|
00000020  6f 6c 74 6f 6e 20 53 6f  66 74 77 61 72 65 20 2d  |olton Software -|
00000030  20 44 65 76 65 6c 6f 70  6d 65 6e 74 2c 20 52 30  | Development, R0|
00000040  31 32 33 20 34 35 36 37  20 38 39 30 31 20 32 33  |123 4567 8901 23|
00000050  34 35 0a 25 4f 50 25 44  50 34 0a 25 4f 50 25 4c  |45.%OP%DP4.%OP%L|
00000060  50 2a 0a 25 4f 50 25 54  4d 34 0a 25 4f 50 25 42  |P*.%OP%TM4.%OP%B|
00000070  4d 34 0a 25 4f 50 25 4c  4d 35 0a 25 4f 50 25 46  |M4.%OP%LM5.%OP%F|
00000080  58 0a 25 4f 50 25 46 59  0a 25 4f 50 25 46 53 0a  |X.%OP%FY.%OP%FS.|
00000090  25 4f 50 25 57 43 32 31  36 2c 31 34 39 32 2c 34  |%OP%WC216,1492,4|
000000a0  36 30 2c 31 32 30 30 2c  30 2c 30 2c 30 2c 30 0a  |60,1200,0,0,0,0.|
000000b0  25 43 4f 3a 41 2c 31 32  2c 31 30 30 25 0a 25 43  |%CO:A,12,100%.%C|
000000c0  25 25 48 31 25 43 6f 6d  70 6c 65 78 20 46 75 6e  |%%H1%Complex Fun|
000000d0  63 74 69 6f 6e 73 20 45  78 61 6d 70 6c 65 73 0a  |ctions Examples.|
000000e0  0a 25 43 25 46 75 6e 63  74 69 6f 6e 0a 0a 20 7a  |.%C%Function.. z|
000000f0  0a 77 0a 7a 2b 77 0a 7a  2d 77 0a 7a 2a 77 0a 7a  |.w.z+w.z-w.z*w.z|
00000100  2f 77 0a 7a 5e 77 0a 65  78 70 28 7a 29 0a 6c 6e  |/w.z^w.exp(z).ln|
00000110  28 7a 29 0a 63 6f 73 28  7a 29 0a 73 69 6e 28 7a  |(z).cos(z).sin(z|
00000120  29 0a 74 61 6e 28 7a 29  0a 61 63 6f 73 28 7a 29  |).tan(z).acos(z)|
00000130  0a 61 73 69 6e 28 7a 29  0a 61 74 61 6e 28 7a 29  |.asin(z).atan(z)|
00000140  0a 63 6f 73 68 28 7a 29  0a 73 69 6e 68 28 7a 29  |.cosh(z).sinh(z)|
00000150  0a 74 61 6e 68 28 7a 29  0a 61 63 6f 73 68 28 7a  |.tanh(z).acosh(z|
00000160  29 0a 61 73 69 6e 68 28  7a 29 0a 61 74 61 6e 68  |).asinh(z).atanh|
00000170  28 7a 29 0a 63 6f 73 65  63 28 7a 29 0a 63 6f 74  |(z).cosec(z).cot|
00000180  28 7a 29 0a 73 65 63 28  7a 29 0a 61 63 6f 73 65  |(z).sec(z).acose|
00000190  63 28 7a 29 0a 61 63 6f  74 28 7a 29 0a 61 73 65  |c(z).acot(z).ase|
000001a0  63 28 7a 29 0a 63 6f 73  65 63 68 28 7a 29 0a 63  |c(z).cosech(z).c|
000001b0  6f 74 68 28 7a 29 0a 73  65 63 68 28 7a 29 0a 61  |oth(z).sech(z).a|
000001c0  63 6f 73 65 63 68 28 7a  29 0a 61 63 6f 74 68 28  |cosech(z).acoth(|
000001d0  7a 29 0a 61 73 65 63 68  28 7a 29 0a 25 43 4f 3a  |z).asech(z).%CO:|
000001e0  42 2c 31 30 2c 30 25 0a  0a 0a 25 52 25 52 65 61  |B,10,0%...%R%Rea|
000001f0  6c 0a 0a 25 56 25 25 52  25 31 0a 25 56 25 25 52  |l..%V%%R%1.%V%%R|
00000200  25 32 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |%2.%V%%R%index(c|
00000210  5f 61 64 64 28 7b 24 42  24 36 2c 24 43 24 36 7d  |_add({$B$6,$C$6}|
00000220  2c 7b 24 42 24 37 2c 24  43 24 37 7d 29 2c 31 2c  |,{$B$7,$C$7}),1,|
00000230  31 29 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |1).%V%%R%index(c|
00000240  5f 73 75 62 28 7b 24 42  24 36 2c 24 43 24 36 7d  |_sub({$B$6,$C$6}|
00000250  2c 7b 24 42 24 37 2c 24  43 24 37 7d 29 2c 31 2c  |,{$B$7,$C$7}),1,|
00000260  31 29 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |1).%V%%R%index(c|
00000270  5f 6d 75 6c 28 7b 24 42  24 36 2c 24 43 24 36 7d  |_mul({$B$6,$C$6}|
00000280  2c 7b 24 42 24 37 2c 24  43 24 37 7d 29 2c 31 2c  |,{$B$7,$C$7}),1,|
00000290  31 29 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |1).%V%%R%index(c|
000002a0  5f 64 69 76 28 7b 24 42  24 36 2c 24 43 24 36 7d  |_div({$B$6,$C$6}|
000002b0  2c 7b 24 42 24 37 2c 24  43 24 37 7d 29 2c 31 2c  |,{$B$7,$C$7}),1,|
000002c0  31 29 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |1).%V%%R%index(c|
000002d0  5f 70 6f 77 65 72 28 7b  24 42 24 36 2c 24 43 24  |_power({$B$6,$C$|
000002e0  36 7d 2c 7b 24 42 24 37  2c 24 43 24 37 7d 29 2c  |6},{$B$7,$C$7}),|
000002f0  31 2c 31 29 0a 25 56 25  25 52 25 69 6e 64 65 78  |1,1).%V%%R%index|
00000300  28 63 5f 65 78 70 28 7b  24 42 24 36 2c 24 43 24  |(c_exp({$B$6,$C$|
00000310  36 7d 29 2c 31 2c 31 29  0a 25 56 25 25 52 25 69  |6}),1,1).%V%%R%i|
00000320  6e 64 65 78 28 63 5f 6c  6e 28 7b 24 42 24 36 2c  |ndex(c_ln({$B$6,|
00000330  24 43 24 36 7d 29 2c 31  2c 31 29 0a 25 56 25 25  |$C$6}),1,1).%V%%|
00000340  52 25 69 6e 64 65 78 28  63 5f 63 6f 73 28 7b 24  |R%index(c_cos({$|
00000350  42 24 36 2c 24 43 24 36  7d 29 2c 31 2c 31 29 0a  |B$6,$C$6}),1,1).|
00000360  25 56 25 25 52 25 69 6e  64 65 78 28 63 5f 73 69  |%V%%R%index(c_si|
00000370  6e 28 7b 24 42 24 36 2c  24 43 24 36 7d 29 2c 31  |n({$B$6,$C$6}),1|
00000380  2c 31 29 0a 25 56 25 25  52 25 69 6e 64 65 78 28  |,1).%V%%R%index(|
00000390  63 5f 74 61 6e 28 7b 24  42 24 36 2c 24 43 24 36  |c_tan({$B$6,$C$6|
000003a0  7d 29 2c 31 2c 31 29 0a  25 56 25 25 52 25 69 6e  |}),1,1).%V%%R%in|
000003b0  64 65 78 28 63 5f 61 63  6f 73 28 7b 24 42 24 36  |dex(c_acos({$B$6|
000003c0  2c 24 43 24 36 7d 29 2c  31 2c 31 29 0a 25 56 25  |,$C$6}),1,1).%V%|
000003d0  25 52 25 69 6e 64 65 78  28 63 5f 61 73 69 6e 28  |%R%index(c_asin(|
000003e0  7b 24 42 24 36 2c 24 43  24 36 7d 29 2c 31 2c 31  |{$B$6,$C$6}),1,1|
000003f0  29 0a 25 56 25 25 52 25  69 6e 64 65 78 28 63 5f  |).%V%%R%index(c_|
00000400  61 74 61 6e 28 7b 24 42  24 36 2c 24 43 24 36 7d  |atan({$B$6,$C$6}|
00000410  29 2c 31 2c 31 29 0a 25  56 25 25 52 25 69 6e 64  |),1,1).%V%%R%ind|
00000420  65 78 28 63 5f 63 6f 73  68 28 7b 24 42 24 36 2c  |ex(c_cosh({$B$6,|
00000430  24 43 24 36 7d 29 2c 31  2c 31 29 0a 25 56 25 25  |$C$6}),1,1).%V%%|
00000440  52 25 69 6e 64 65 78 28  63 5f 73 69 6e 68 28 7b  |R%index(c_sinh({|
00000450  24 42 24 36 2c 24 43 24  36 7d 29 2c 31 2c 31 29  |$B$6,$C$6}),1,1)|
00000460  0a 25 56 25 25 52 25 69  6e 64 65 78 28 63 5f 74  |.%V%%R%index(c_t|
00000470  61 6e 68 28 7b 24 42 24  36 2c 24 43 24 36 7d 29  |anh({$B$6,$C$6})|
00000480  2c 31 2c 31 29 0a 25 56  25 25 52 25 69 6e 64 65  |,1,1).%V%%R%inde|
00000490  78 28 63 5f 61 63 6f 73  68 28 7b 24 42 24 36 2c  |x(c_acosh({$B$6,|
000004a0  24 43 24 36 7d 29 2c 31  2c 31 29 0a 25 56 25 25  |$C$6}),1,1).%V%%|
000004b0  52 25 69 6e 64 65 78 28  63 5f 61 73 69 6e 68 28  |R%index(c_asinh(|
000004c0  7b 24 42 24 36 2c 24 43  24 36 7d 29 2c 31 2c 31  |{$B$6,$C$6}),1,1|
000004d0  29 0a 25 56 25 25 52 25  69 6e 64 65 78 28 63 5f  |).%V%%R%index(c_|
000004e0  61 74 61 6e 68 28 7b 24  42 24 36 2c 24 43 24 36  |atanh({$B$6,$C$6|
000004f0  7d 29 2c 31 2c 31 29 0a  25 56 25 25 52 25 69 6e  |}),1,1).%V%%R%in|
00000500  64 65 78 28 63 5f 63 6f  73 65 63 28 7b 24 42 24  |dex(c_cosec({$B$|
00000510  36 2c 24 43 24 36 7d 29  2c 31 2c 31 29 0a 25 56  |6,$C$6}),1,1).%V|
00000520  25 25 52 25 69 6e 64 65  78 28 63 5f 63 6f 74 28  |%%R%index(c_cot(|
00000530  7b 24 42 24 36 2c 24 43  24 36 7d 29 2c 31 2c 31  |{$B$6,$C$6}),1,1|
00000540  29 0a 25 56 25 25 52 25  69 6e 64 65 78 28 63 5f  |).%V%%R%index(c_|
00000550  73 65 63 28 7b 24 42 24  36 2c 24 43 24 36 7d 29  |sec({$B$6,$C$6})|
00000560  2c 31 2c 31 29 0a 25 56  25 25 52 25 69 6e 64 65  |,1,1).%V%%R%inde|
00000570  78 28 63 5f 61 63 6f 73  65 63 28 7b 24 42 24 36  |x(c_acosec({$B$6|
00000580  2c 24 43 24 36 7d 29 2c  31 2c 31 29 0a 25 56 25  |,$C$6}),1,1).%V%|
00000590  25 52 25 69 6e 64 65 78  28 63 5f 61 63 6f 74 28  |%R%index(c_acot(|
000005a0  7b 24 42 24 36 2c 24 43  24 36 7d 29 2c 31 2c 31  |{$B$6,$C$6}),1,1|
000005b0  29 0a 25 56 25 25 52 25  69 6e 64 65 78 28 63 5f  |).%V%%R%index(c_|
000005c0  61 73 65 63 28 7b 24 42  24 36 2c 24 43 24 36 7d  |asec({$B$6,$C$6}|
000005d0  29 2c 31 2c 31 29 0a 25  56 25 25 52 25 69 6e 64  |),1,1).%V%%R%ind|
000005e0  65 78 28 63 5f 63 6f 73  65 63 68 28 7b 24 42 24  |ex(c_cosech({$B$|
000005f0  36 2c 24 43 24 36 7d 29  2c 31 2c 31 29 0a 25 56  |6,$C$6}),1,1).%V|
00000600  25 25 52 25 69 6e 64 65  78 28 63 5f 63 6f 74 68  |%%R%index(c_coth|
00000610  28 7b 24 42 24 36 2c 24  43 24 36 7d 29 2c 31 2c  |({$B$6,$C$6}),1,|
00000620  31 29 0a 25 56 25 25 52  25 69 6e 64 65 78 28 63  |1).%V%%R%index(c|
00000630  5f 73 65 63 68 28 7b 24  42 24 36 2c 24 43 24 36  |_sech({$B$6,$C$6|
00000640  7d 29 2c 31 2c 31 29 0a  25 56 25 25 52 25 69 6e  |}),1,1).%V%%R%in|
00000650  64 65 78 28 63 5f 61 63  6f 73 65 63 68 28 7b 24  |dex(c_acosech({$|
00000660  42 24 36 2c 24 43 24 36  7d 29 2c 31 2c 31 29 0a  |B$6,$C$6}),1,1).|
00000670  25 56 25 25 52 25 69 6e  64 65 78 28 63 5f 61 63  |%V%%R%index(c_ac|
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00001310  65 73 20 6f 6e 65 20 63  6f 6d 70 6c 65 78 20 6e  |es one complex n|
00001320  75 6d 62 65 72 20 62 79  20 61 6e 6f 74 68 65 72  |umber by another|
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00001340  70 6c 65 78 20 6e 75 6d  62 65 72 20 74 6f 20 74  |plex number to t|
00001350  68 65 20 70 6f 77 65 72  20 6f 66 20 61 6e 6f 74  |he power of anot|
00001360  68 65 72 2e 0a 52 61 69  73 65 73 20 65 20 28 6e  |her..Raises e (n|
00001370  61 74 75 72 61 6c 20 65  78 70 6f 6e 65 6e 74 29  |atural exponent)|
00001380  20 74 6f 20 74 68 65 20  70 6f 77 65 72 20 6f 66  | to the power of|
00001390  20 61 20 63 6f 6d 70 6c  65 78 20 6e 75 6d 62 65  | a complex numbe|
000013a0  72 2e 0a 52 65 74 75 72  6e 73 20 74 68 65 20 6e  |r..Returns the n|
000013b0  61 74 75 72 61 6c 20 6c  6f 67 61 72 69 74 68 6d  |atural logarithm|
000013c0  20 6f 66 20 61 20 63 6f  6d 70 6c 65 78 20 6e 75  | of a complex nu|
000013d0  6d 62 65 72 2e 0a 52 65  74 75 72 6e 73 20 74 68  |mber..Returns th|
000013e0  65 20 43 6f 73 69 6e 65  20 6f 66 20 61 20 63 6f  |e Cosine of a co|
000013f0  6d 70 6c 65 78 20 6e 75  6d 62 65 72 2e 0a 52 65  |mplex number..Re|
00001400  74 75 72 6e 73 20 74 68  65 20 53 69 6e 65 20 6f  |turns the Sine o|
00001410  66 20 61 20 63 6f 6d 70  6c 65 78 20 6e 75 6d 62  |f a complex numb|
00001420  65 72 2e 0a 52 65 74 75  72 6e 73 20 74 68 65 20  |er..Returns the |
00001430  54 61 6e 67 65 6e 74 20  6f 66 20 61 20 63 6f 6d  |Tangent of a com|
00001440  70 6c 65 78 20 6e 75 6d  62 65 72 2e 0a 52 65 74  |plex number..Ret|
00001450  75 72 6e 73 20 74 68 65  20 69 6e 76 65 72 73 65  |urns the inverse|
00001460  20 43 6f 73 69 6e 65 20  6f 66 20 61 20 63 6f 6d  | Cosine of a com|
00001470  70 6c 65 78 20 6e 75 6d  62 65 72 2e 0a 52 65 74  |plex number..Ret|
00001480  75 72 6e 73 20 74 68 65  20 69 6e 76 65 72 73 65  |urns the inverse|
00001490  20 53 69 6e 65 20 6f 66  20 61 20 63 6f 6d 70 6c  | Sine of a compl|
000014a0  65 78 20 6e 75 6d 62 65  72 2e 0a 52 65 74 75 72  |ex number..Retur|
000014b0  6e 73 20 74 68 65 20 69  6e 76 65 72 73 65 20 54  |ns the inverse T|
000014c0  61 6e 67 65 6e 74 20 6f  66 20 61 20 63 6f 6d 70  |angent of a comp|
000014d0  6c 65 78 20 6e 75 6d 62  65 72 2e 0a 52 65 74 75  |lex number..Retu|
000014e0  72 6e 73 20 74 68 65 20  68 79 70 65 72 62 6f 6c  |rns the hyperbol|
000014f0  69 63 20 43 6f 73 69 6e  65 20 6f 66 20 61 20 63  |ic Cosine of a c|
00001500  6f 6d 70 6c 65 78 20 6e  75 6d 62 65 72 2e 0a 52  |omplex number..R|
00001510  65 74 75 72 6e 73 20 74  68 65 20 68 79 70 65 72  |eturns the hyper|
00001520  62 6f 6c 69 63 20 53 69  6e 65 20 6f 66 20 61 20  |bolic Sine of a |
00001530  63 6f 6d 70 6c 65 78 20  6e 75 6d 62 65 72 2e 0a  |complex number..|
00001540  52 65 74 75 72 6e 73 20  74 68 65 20 68 79 70 65  |Returns the hype|
00001550  72 62 6f 6c 69 63 20 54  61 6e 67 65 6e 74 20 6f  |rbolic Tangent o|
00001560  66 20 61 20 63 6f 6d 70  6c 65 78 20 6e 75 6d 62  |f a complex numb|
00001570  65 72 2e 0a 52 65 74 75  72 6e 73 20 74 68 65 20  |er..Returns the |
00001580  69 6e 76 65 72 73 65 20  68 79 70 65 72 62 6f 6c  |inverse hyperbol|
00001590  69 63 20 43 6f 73 69 6e  65 20 6f 66 20 61 20 63  |ic Cosine of a c|
000015a0  6f 6d 70 6c 65 78 20 6e  75 6d 62 65 72 2e 0a 52  |omplex number..R|
000015b0  65 74 75 72 6e 73 20 74  68 65 20 69 6e 76 65 72  |eturns the inver|
000015c0  73 65 20 68 79 70 65 72  62 6f 6c 69 63 20 53 69  |se hyperbolic Si|
000015d0  6e 65 20 6f 66 20 61 20  63 6f 6d 70 6c 65 78 20  |ne of a complex |
000015e0  6e 75 6d 62 65 72 2e 0a  52 65 74 75 72 6e 73 20  |number..Returns |
000015f0  74 68 65 20 69 6e 76 65  72 73 65 20 68 79 70 65  |the inverse hype|
00001600  72 62 6f 6c 69 63 20 54  61 6e 67 65 6e 74 20 6f  |rbolic Tangent o|
00001610  66 20 61 20 63 6f 6d 70  6c 65 78 20 6e 75 6d 62  |f a complex numb|
00001620  65 72 2e 0a 52 65 74 75  72 6e 73 20 74 68 65 20  |er..Returns the |
00001630  43 6f 73 65 63 61 6e 74  20 6f 66 20 61 20 63 6f  |Cosecant of a co|
00001640  6d 70 6c 65 78 20 6e 75  6d 62 65 72 2e 0a 52 65  |mplex number..Re|
00001650  74 75 72 6e 73 20 74 68  65 20 43 6f 74 61 6e 67  |turns the Cotang|
00001660  65 6e 74 20 6f 66 20 61  20 63 6f 6d 70 6c 65 78  |ent of a complex|
00001670  20 6e 75 6d 62 65 72 2e  0a 52 65 74 75 72 6e 73  | number..Returns|
00001680  20 74 68 65 20 53 65 63  61 6e 74 20 6f 66 20 61  | the Secant of a|
00001690  20 63 6f 6d 70 6c 65 78  20 6e 75 6d 62 65 72 2e  | complex number.|
000016a0  0a 52 65 74 75 72 6e 73  20 74 68 65 20 69 6e 76  |.Returns the inv|
000016b0  65 72 73 65 20 43 6f 73  65 63 61 6e 74 20 6f 66  |erse Cosecant of|
000016c0  20 61 20 63 6f 6d 70 6c  65 78 20 6e 75 6d 62 65  | a complex numbe|
000016d0  72 2e 0a 52 65 74 75 72  6e 73 20 74 68 65 20 69  |r..Returns the i|
000016e0  6e 76 65 72 73 65 20 43  6f 74 61 6e 67 65 6e 74  |nverse Cotangent|
000016f0  20 6f 66 20 61 20 63 6f  6d 70 6c 65 78 20 6e 75  | of a complex nu|
00001700  6d 62 65 72 2e 0a 52 65  74 75 72 6e 73 20 74 68  |mber..Returns th|
00001710  65 20 69 6e 76 65 72 73  65 20 53 65 63 61 6e 74  |e inverse Secant|
00001720  20 6f 66 20 61 20 63 6f  6d 70 6c 65 78 20 6e 75  | of a complex nu|
00001730  6d 62 65 72 2e 0a 52 65  74 75 72 6e 73 20 74 68  |mber..Returns th|
00001740  65 20 68 79 70 65 72 62  6f 6c 69 63 20 43 6f 73  |e hyperbolic Cos|
00001750  65 63 61 6e 74 20 6f 66  20 61 20 63 6f 6d 70 6c  |ecant of a compl|
00001760  65 78 20 6e 75 6d 62 65  72 2e 0a 52 65 74 75 72  |ex number..Retur|
00001770  6e 73 20 74 68 65 20 68  79 70 65 72 62 6f 6c 69  |ns the hyperboli|
00001780  63 20 43 6f 74 61 6e 67  65 6e 74 20 6f 66 20 61  |c Cotangent of a|
00001790  20 63 6f 6d 70 6c 65 78  20 6e 75 6d 62 65 72 2e  | complex number.|
000017a0  0a 52 65 74 75 72 6e 73  20 74 68 65 20 68 79 70  |.Returns the hyp|
000017b0  65 72 62 6f 6c 69 63 20  53 65 63 61 6e 74 20 6f  |erbolic Secant o|
000017c0  66 20 61 20 63 6f 6d 70  6c 65 78 20 6e 75 6d 62  |f a complex numb|
000017d0  65 72 2e 0a 52 65 74 75  72 6e 73 20 74 68 65 20  |er..Returns the |
000017e0  69 6e 76 65 72 73 65 20  68 79 70 65 72 62 6f 6c  |inverse hyperbol|
000017f0  69 63 20 43 6f 73 65 63  61 6e 74 20 6f 66 20 61  |ic Cosecant of a|
00001800  20 63 6f 6d 70 6c 65 78  20 6e 75 6d 62 65 72 2e  | complex number.|
00001810  0a 52 65 74 75 72 6e 73  20 74 68 65 20 69 6e 76  |.Returns the inv|
00001820  65 72 73 65 20 68 79 70  65 72 62 6f 6c 69 63 20  |erse hyperbolic |
00001830  43 6f 74 61 6e 67 65 6e  74 20 6f 66 20 61 20 63  |Cotangent of a c|
00001840  6f 6d 70 6c 65 78 20 6e  75 6d 62 65 72 2e 0a 52  |omplex number..R|
00001850  65 74 75 72 6e 73 20 74  68 65 20 69 6e 76 65 72  |eturns the inver|
00001860  73 65 20 68 79 70 65 72  62 6f 6c 69 63 20 53 65  |se hyperbolic Se|
00001870  63 61 6e 74 20 6f 66 20  61 20 63 6f 6d 70 6c 65  |cant of a comple|
00001880  78 20 6e 75 6d 62 65 72  2e 0a                    |x number..|
0000188a