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# Complex Numbers

Contents:

1. Class methods

2. Properties of Complex Numbers

3. Complex Arithmetic Operators

4. Elementary Complex Functions

5. Complex Trigonometric Functions

6. Inverse Complex Trigonometric Functions

7. Complex Hyperbolic Functions

8. Inverse Complex Hyperbolic Functions

## Class Methods

- GSL::Complex.alloc(re, im)

- GSL::Complex.rect(re, im)

- GSL::Complex[re, im]

  These create a GSL::Complex object with real and imaginary part `re, im`.

- GSL::Complex.polar(r, theta)

  This returns a GSL::Complex object in polar representation, with the amplitude `r` and the phase (argument) `theta`.

## Properties of complex numbers

- GSL::Complex#real

- GSL::Complex#re

- GSL::Complex#REAL

  Returns the real part

- GSL::Complex#imag

- GSL::Complex#im

- GSL::Complex#IMAG

  Returns the imaginary part

- GSL::Complex#arg

- GSL::Complex#angle

- GSL::Complex#phase

  Returns the argument (i.e. phase angle in radians) of `self`.

- GSL::Complex#abs, abs2, logabs

  Returns the magnitude, squared magnitude, and the logarithm of the magnitude

## Complex arithmetic operators

- GSL::Complex#add(b)

- GSL::Complex#+(b)

  Return the sum of the complex numbers `self` and `b`.

- GSL::Complex#sub(b)

- GSL::Complex#-(b)

  Return the difference of the complex numbers `self` and `b`.

- GSL::Complex#mul(b)

- GSL::Complex#*(b)

  Returns the product of the complex numbers `self` and `b`.

- GSL::Complex#div(b)

- GSL::Complex#/(b)

  Returns the quotient of the complex numbers `self` and `b`.

- GSL::Complex#add_real

- GSL::Complex#sub_real

- GSL::Complex#mul_real

- GSL::Complex#div_real

- GSL::Complex#add_imag

- GSL::Complex#sub_imag

- GSL::Complex#mul_imag

- GSL::Complex#div_imag

- GSL::Complex#conjugate

- GSL::Complex#conj

  Returns the complex conjugate of the complex number `self`.

- GSL::Complex#inverse

  Returns the inverse of the complex number `self`.

- GSL::Complex#negative

  Returns the negative of the complex number `self`.

## Elementary Complex Functions

- GSL::Complex#sqrt

- GSL::Complex#pow(az)

- GSL::Complex#pow_real(a)

- GSL::Complex#exp

- GSL::Complex#log

- GSL::Complex#log10

- GSL::Complex#log_b(b)

- GSL::Complex.sqrt(z)

- GSL::Complex.sqrt_real(a)

- GSL::Complex.pow(z, za)

- GSL::Complex.pow_real(z, a)

- GSL::Complex.exp(z)

- GSL::Complex.log(z)

- GSL::Complex.log10(z)

- GSL::Complex.log_b(z, b)

## Complex Trigonometric Functions

- GSL::Complex#sin

- GSL::Complex#cos

- GSL::Complex#tan

- GSL::Complex#sec

- GSL::Complex#csc

- GSL::Complex#cot

- GSL::Complex.sin(z)

- GSL::Complex.cos(z)

- GSL::Complex.tan(z)

- GSL::Complex.sec(z)

- GSL::Complex.csc(z)

- GSL::Complex.cot(z)

## Inverse Complex Trigonometric Functions

- GSL::Complex#arcsin

- GSL::Complex#arccos

- GSL::Complex#arctan

- GSL::Complex#arcsec

- GSL::Complex#arccsc

- GSL::Complex#arccot

- GSL::Complex.arcsin(z)

- GSL::Complex.arcsin_real(a)

- GSL::Complex.arccos(z)

- GSL::Complex.arccos_real(a)

- GSL::Complex.arctan(z)

- GSL::Complex.arcsec(z)

- GSL::Complex.arcsec_real(a)

- GSL::Complex.arccsc(z)

- GSL::Complex.arccsc_real(z)

- GSL::Complex.arccot(z)

## Complex Hyperbolic Functions

- GSL::Complex#sinh

- GSL::Complex#cosh

- GSL::Complex#tanh

- GSL::Complex#sech

- GSL::Complex#csch

- GSL::Complex#coth

- GSL::Complex.sinh(z)

- GSL::Complex.cosh(z)

- GSL::Complex.tanh(z)

- GSL::Complex.sech(z)

- GSL::Complex.csch(z)

- GSL::Complex.coth(z)

## Inverse Complex Hyperbolic Functions

- GSL::Complex#arcsinh

- GSL::Complex#arccosh

- GSL::Complex#arctanh

- GSL::Complex#arcsech

- GSL::Complex#arccsch

- GSL::Complex#arccoth

- GSL::Complex#arcsinh(z)

- GSL::Complex#arccosh(z)

- GSL::Complex#arccosh_real(a)

- GSL::Complex#arctanh(z)

- GSL::Complex#arctanh_real(z)

- GSL::Complex#arcsech(z)

- GSL::Complex#arccsch(z)

- GSL::Complex#arccoth(z)

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