What is the complex conjugate of number 12+5i?

1 Answer
Jul 9, 2015

Answer:

The complex conjugate of #(12+5i)# is #(12-5i)#

Explanation:

The complex conjugate is the value you need to multiply a given complex number by

  • to eradicate the imaginary component
  • using the concept of difference of squares:
    #color(white)("XXXX")##(a^2-b^2) = (a+b)(a-b)#
    #color(white)("XXXX")#or, for complex numbers:
    #color(white)("XXXX")##(a^2+b^2) = (a^2-(bi)^2) = (a+bi)(a-bi)#

That is
#color(white)("XXXX")##(a+bi)# and #(a-bi)# are complex conjugates of each other.