Complex conjugate
Given a complex number, find its complex conjugate. By definition, the complex conjugate of is (where and are real numbers, and is the square root of -1).
Some languages have complex number libraries available. If possible, use your library's operation for complex conjugate.
Factor
<lang factor>USING: math.functions prettyprint ;
C{ 2 3 } conjugate . ! prints C{ 2 -3 } C{ 4 -5 } conjugate . ! prints C{ 4 5 }</lang>
Ruby
<lang ruby>require 'complex' # With Ruby 1.9, this line is optional.
- Complex#conj or Complex#conjugate finds the conjugate.
i = Complex::I puts (2 + 3*i).conj # 2-3i puts (4 - 5*i).conjugate # 4+5i
- Numeric#conj or Numeric#conjugate returns self.
puts 67.conjugate # 67</lang>
Tcl
<lang tcl>package require math::complexnumbers namespace import math::complexnumbers::* foreach x {{2 3} {4 -5} {67 0}} {
set c [complex {*}$x] puts "[tostring $c] conjucate is [tostring [conj $c]]"
}</lang> Produces the output
2+3i conjucate is 2-3i 4-5i conjucate is 4+5i 67 conjucate is 67