How do you divide #(2-3i)(5i) /(2+3i)#?

1 Answer
Daniel L.
Oct 24, 2015

#(2-3i)((5i)/(2+3i))=60-25i#

Explanation:

First step is to multiply #(2-3i)# by #5i#:

#(2-3i)((5i)/(2+3i))=(10i+15)/(2+3i)=(5(3+2i))/(2+3i)#

Next step is to expand the fraction by complex conjugate of the denominator. In this way we get a real number in the denominator.

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

#=(5(12-5i))/(4-3)=60-25i#

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