# complex

This module implements complex numbers. Complex numbers are currently implemented as generic on a 64-bit or 32-bit float.

math

# Types

```Complex[T] = object
re*, im*: T                ## A complex number, consisting of a real and an imaginary part.
```
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`Complex64 = Complex[float64]`
Alias for a pair of 64-bit floats.   Source Edit
`Complex32 = Complex[float32]`
Alias for a pair of 32-bit floats.   Source Edit

# Procs

`proc complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]`
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```proc complex32(re: float32; im: float32 = 0.0): Complex[float32] {...}{.raises: [],
tags: [].}```
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```proc complex64(re: float64; im: float64 = 0.0): Complex[float64] {...}{.raises: [],
tags: [].}```
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`proc abs[T](z: Complex[T]): T`
Return the distance from (0,0) to z.   Source Edit
`proc abs2[T](z: Complex[T]): T`
Return the squared distance from (0,0) to z.   Source Edit
`proc conjugate[T](z: Complex[T]): Complex[T]`
Conjugate of complex number z.   Source Edit
`proc inv[T](z: Complex[T]): Complex[T]`
Multiplicative inverse of complex number z.   Source Edit
`proc `==`[T](x, y: Complex[T]): bool`
Compare two complex numbers x and y for equality.   Source Edit
`proc `+`[T](x: T; y: Complex[T]): Complex[T]`
Add a real number to a complex number.   Source Edit
`proc `+`[T](x: Complex[T]; y: T): Complex[T]`
Add a complex number to a real number.   Source Edit
`proc `+`[T](x, y: Complex[T]): Complex[T]`
Add two complex numbers.   Source Edit
`proc `-`[T](z: Complex[T]): Complex[T]`
Unary minus for complex numbers.   Source Edit
`proc `-`[T](x: T; y: Complex[T]): Complex[T]`
Subtract a complex number from a real number.   Source Edit
`proc `-`[T](x: Complex[T]; y: T): Complex[T]`
Subtract a real number from a complex number.   Source Edit
`proc `-`[T](x, y: Complex[T]): Complex[T]`
Subtract two complex numbers.   Source Edit
`proc `/`[T](x: Complex[T]; y: T): Complex[T]`
Divide complex number x by real number y.   Source Edit
`proc `/`[T](x: T; y: Complex[T]): Complex[T]`
Divide real number x by complex number y.   Source Edit
`proc `/`[T](x, y: Complex[T]): Complex[T]`
Divide x by y.   Source Edit
`proc `*`[T](x: T; y: Complex[T]): Complex[T]`
Multiply a real number and a complex number.   Source Edit
`proc `*`[T](x: Complex[T]; y: T): Complex[T]`
Multiply a complex number with a real number.   Source Edit
`proc `*`[T](x, y: Complex[T]): Complex[T]`
Multiply x with y.   Source Edit
`proc `+=`[T](x: var Complex[T]; y: Complex[T])`
Add y to x.   Source Edit
`proc `-=`[T](x: var Complex[T]; y: Complex[T])`
Subtract y from x.   Source Edit
`proc `*=`[T](x: var Complex[T]; y: Complex[T])`
Multiply y to x.   Source Edit
`proc `/=`[T](x: var Complex[T]; y: Complex[T])`
Divide x by y in place.   Source Edit
`proc sqrt[T](z: Complex[T]): Complex[T]`
Square root for a complex number z.   Source Edit
`proc exp[T](z: Complex[T]): Complex[T]`
e raised to the power z.   Source Edit
`proc ln[T](z: Complex[T]): Complex[T]`
Returns the natural log of z.   Source Edit
`proc log10[T](z: Complex[T]): Complex[T]`
Returns the log base 10 of z.   Source Edit
`proc log2[T](z: Complex[T]): Complex[T]`
Returns the log base 2 of z.   Source Edit
`proc pow[T](x, y: Complex[T]): Complex[T]`
x raised to the power y.   Source Edit
`proc pow[T](x: Complex[T]; y: T): Complex[T]`
Complex number x raised to the power y.   Source Edit
`proc sin[T](z: Complex[T]): Complex[T]`
Returns the sine of z.   Source Edit
`proc arcsin[T](z: Complex[T]): Complex[T]`
Returns the inverse sine of z.   Source Edit
`proc cos[T](z: Complex[T]): Complex[T]`
Returns the cosine of z.   Source Edit
`proc arccos[T](z: Complex[T]): Complex[T]`
Returns the inverse cosine of z.   Source Edit
`proc tan[T](z: Complex[T]): Complex[T]`
Returns the tangent of z.   Source Edit
`proc arctan[T](z: Complex[T]): Complex[T]`
Returns the inverse tangent of z.   Source Edit
`proc cot[T](z: Complex[T]): Complex[T]`
Returns the cotangent of z.   Source Edit
`proc arccot[T](z: Complex[T]): Complex[T]`
Returns the inverse cotangent of z.   Source Edit
`proc sec[T](z: Complex[T]): Complex[T]`
Returns the secant of z.   Source Edit
`proc arcsec[T](z: Complex[T]): Complex[T]`
Returns the inverse secant of z.   Source Edit
`proc csc[T](z: Complex[T]): Complex[T]`
Returns the cosecant of z.   Source Edit
`proc arccsc[T](z: Complex[T]): Complex[T]`
Returns the inverse cosecant of z.   Source Edit
`proc sinh[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic sine of z.   Source Edit
`proc arcsinh[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic sine of z.   Source Edit
`proc cosh[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic cosine of z.   Source Edit
`proc arccosh[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic cosine of z.   Source Edit
`proc tanh[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic tangent of z.   Source Edit
`proc arctanh[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic tangent of z.   Source Edit
`proc sech[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic secant of z.   Source Edit
`proc arcsech[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic secant of z.   Source Edit
`proc csch[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic cosecant of z.   Source Edit
`proc arccsch[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic cosecant of z.   Source Edit
`proc coth[T](z: Complex[T]): Complex[T]`
Returns the hyperbolic cotangent of z.   Source Edit
`proc arccoth[T](z: Complex[T]): Complex[T]`
Returns the inverse hyperbolic cotangent of z.   Source Edit
`proc phase[T](z: Complex[T]): T`
Returns the phase of z.   Source Edit
`proc polar[T](z: Complex[T]): tuple[r, phi: T]`
Returns z in polar coordinates.   Source Edit
`proc rect[T](r, phi: T): Complex[T]`
Returns the complex number with polar coordinates r and phi.

result.re = r * cos(phi)
result.im = r * sin(phi)

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`proc `\$`(z: Complex): string`
Returns z's string representation as "(re, im)".   Source Edit

# Templates

`template im(arg: typedesc[float32]): Complex32`
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`template im(arg: typedesc[float64]): Complex64`
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`template im(arg: float32): Complex32`
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`template im(arg: float64): Complex64`
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