SOLUTION: Divide. (4+2i)/(5-6i) Write your answer as a complex number in standard form.

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Question 451157: Divide.
(4+2i)/(5-6i)

Write your answer as a complex number in standard form.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284%2B2i%29%2F%285-6i%29 Start with the given expression.


%28%284%2B2i%29%2F%285-6i%29%29%28%285%2B6i%29%2F%285%2B6i%29%29 Multiply the fraction by %285%2B6i%29%2F%285%2B6i%29.


%28%284%2B2i%29%285%2B6i%29%29%2F%28%285-6i%29%285%2B6i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2820%2B24i%2B10i%2B12i%5E2%29%2F%2825%2B30i-30i-36i%5E2%29 Multiply.


%2820%2B24i%2B10i%2B12%28-1%29%29%2F%2825%2B30i-30i-36%28-1%29%29 Replace i%5E2 with -1.


%2820%2B24i%2B10i-12%29%2F%2825%2B30i-30i%2B36%29 Multiply.


%288%2B34i%29%2F%2861%29 Combine like terms.


%288%29%2F%2861%29%2B%28%2834%29%2F%2861%29%29i Break up the fraction.


8%2F61%2B%2834%2F61%29i Reduce.


So %284%2B2i%29%2F%285-6i%29=8%2F61%2B%2834%2F61%29i.


So the expression is now in standard form a%2Bbi where a=8%2F61 and b=34%2F61