SOLUTION: Please help me with this. Divide as indicated. Write the quotient in standard form. 6+3i divided by 4-3i

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Question 316763: Please help me with this. Divide as indicated. Write the quotient in standard form.
6+3i divided by 4-3i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%286%2B3i%29%2F%284-3i%29 Start with the given expression.


%28%286%2B3i%29%2F%284-3i%29%29%28%284%2B3i%29%2F%284%2B3i%29%29 Multiply the fraction by %284%2B3i%29%2F%284%2B3i%29.


%28%286%2B3i%29%284%2B3i%29%29%2F%28%284-3i%29%284%2B3i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2824%2B18i%2B12i%2B9i%5E2%29%2F%2816%2B12i-12i-9i%5E2%29 Multiply.


%2824%2B18i%2B12i%2B9%28-1%29%29%2F%2816%2B12i-12i-9%28-1%29%29 Replace i%5E2 with -1.


%2824%2B18i%2B12i-9%29%2F%2816%2B12i-12i%2B9%29 Multiply.


%2815%2B30i%29%2F%2825%29 Combine like terms.


%2815%29%2F%2825%29%2B%28%2830%29%2F%2825%29%29i Break up the fraction.


3%2F5%2B%286%2F5%29i Reduce.


So %286%2B3i%29%2F%284-3i%29=3%2F5%2B%286%2F5%29i.


So the expression is now in standard form a%2Bbi where a=3%2F5 and b=6%2F5