How do you simplify #(5-3i)/(1+2i)#?

1 Answer
sente
Nov 20, 2015

#(5-3i)/(1+2i) = -(1+13i)/5#

Explanation:

To simplify a fraction with a complex number in the denominator, we simply multiply the numerator and the denominator by the complex conjugate of the denominator.

#(5-3i)/(1+2i)= (5-3i)/(1+2i)*(1-2i)/(1-2i)#

Note that this will leave us with a real number for the denominator.

# (5-3i)/(1+2i)*(1-2i)/(1-2i)=(5 -10i -3i -6)/(1 -2i +2i +4) = -(1+13i)/5#

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