# Ruby: Complex Numbers

In Ruby, Complex number is represented by the object “Complex”. Example:

# -*- coding: utf-8 -*- # ruby # a complex number cc = Complex(3, 4) # when printed, it's shown as (x+y i) p cc # (3+4i)

## Get Real and Imaginary Parts

# -*- coding: utf-8 -*- # ruby # a complex number cc = Complex(3, 4) p cc.real # 3 p cc.imag # 4

## Complex Number Addition, Multiplication

# -*- coding: utf-8 -*- # ruby # Complex number addition. (same as vector addition) p Complex(2, 3) + Complex(4, 5) # (6+8i) # multiplication of complex numbers p Complex(1, 0) * Complex(0, 1) # (0+1i) # scalar multiplication. That is, scale it. p Complex(3, 4) * 2 # (6+8j) # adding a scalar adds to the real part p Complex(3, 4) + 1 # (4+4i)

## Get Complex Number Length

# -*- coding: utf-8 -*- # ruby # length of a Complex number p Complex(3, 4).abs # 5.0

## Get Complex Number Angle

# -*- coding: utf-8 -*- # ruby z1 = Complex(0, 1) # get the angle. return in radians p z1.angle # 1.5707963267948966

## Convert To/From Rectangular, Polar Coordinates

# -*- coding: utf-8 -*- # ruby length = 1 angle = Math::PI # polar to rectangular coordinate p Complex.polar(length, angle) # (-1+0.0i)

# -*- coding: utf-8 -*- # ruby z1 = Complex(0, 1) # rectangular to polar coordinates. Returns a array [length, angle] p z1.polar # [1, 1.5707963267948966]

http://www.ruby-doc.org/core-1.9.3/Complex.html

## π and e

π is `Math::PI`

e is `Math::E`

# coding: utf-8 # ruby # constant π p Math::PI # 3.141592653589793 # constant e p Math::E # 2.718281828459045

http://www.ruby-doc.org/core-1.9.3/Math.html

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