How do you simplify #( 3-2i)/(3+2i )#?

1 Answer
sente
May 18, 2016

#(3-2i)/(3+2i)=5/13-12/13i#

Explanation:

Given a complex number #a+bi#, the complex conjugate of that number is #a-bi#. A useful property is that the product of any number with its complex conjugate is a real number. We will use that to eliminate the complex number from the denominator.

#(3-2i)/(3+2i) = ((3-2i)(3-2i))/((3+2i)(3-2i))#

#=(5-12i)/13#

#=5/13-12/13i#

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