Title: 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

1 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.

2 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#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

3 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
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.

4 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)

5 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)

6 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)

7 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)

8 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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