Complex Numbers

# Title: Complex Numbers

## 1 Class Methods

`GSL::Complex.new(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.

## 2 Methods

`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#set(re, im)`
`GSL::Complex#set_complex(re, im)`
`GSL::Complex#SET_COMPLEX(re, im)`
  Set the real and imaginary parts of the complex number.
`GSL::Complex#set_real(re)`
`GSL::Complex#set_re(re)`
`GSL::Complex#SET_REAL(re)`
`GSL::Complex#real=(re)`
`GSL::Complex#re=(re)`
`GSL::Complex#set_imag(im)`
`GSL::Complex#set_im(im)`
`GSL::Complex#SET_IMAG(im)`
`GSL::Complex#imag=(im)`
`GSL::Complex#im=(im)`
  Set the real or imaginary parts of the complex number.
`GSL::Complex#arg`
  Returns the argument
`GSL::Complex#abs, abs2, logabs`
  Returns the magnitude, squared magnitude, and the logarithm of the magnitude

### 2.1 Complex arithmetic

`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`
  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.

### 2.2 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)`

### 2.3 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)`

### 2.4 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)`

### 2.5 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)`

### 2.6 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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