Ruby: Complex Numbers
In Ruby, Complex number is represented by the object “Complex”. Example:
# 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
# ruby # a complex number cc = Complex(3, 4) p cc.real # 3 p cc.imag # 4
Complex Number Addition, Multiplication
# 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
# ruby # length of a Complex number p Complex(3, 4).abs # 5.0
Get Complex Number Angle
# ruby z1 = Complex(0, 1) # get the angle. return in radians p z1.angle # 1.5707963267948966
Convert To/From Rectangular, Polar Coordinates
# ruby length = 1 angle = Math::PI # polar to rectangular coordinate p Complex.polar(length, angle) # (-1+0.0i)
# 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