SOLUTION: Simplify the following quotient of complex numbers into the form a + bi. -9+2i/-8-(9i)= I have no idea where to start~ Please help!

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Question 602132: Simplify the following quotient of complex numbers into the form a + bi.
-9+2i/-8-(9i)=
I have no idea where to start~ Please help!



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28-9%2B2i%29%2F%28-8-9i%29 Start with the given expression.


%28%28-9%2B2i%29%2F%28-8-9i%29%29%28%28-8%2B9i%29%2F%28-8%2B9i%29%29 Multiply the fraction by %28-8%2B9i%29%2F%28-8%2B9i%29.


%28%28-9%2B2i%29%28-8%2B9i%29%29%2F%28%28-8-9i%29%28-8%2B9i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2872-81i-16i%2B18i%5E2%29%2F%2864-72i%2B72i-81i%5E2%29 Multiply.


%2872-81i-16i%2B18i%5E2%29%2F%2864-72i%2B72i-81%28-1%29%29 Replace i%5E2 with -1.


%2872-81i-16i%2B18i%5E2%29%2F%2864-72i%2B72i%2B81%29 Multiply


%2854-97i%29%2F%28145%29 Combine like terms.


%2854%29%2F%28145%29%2B%28%28-97%29%2F%28145%29%29i Break up the fraction.


54%2F145-%2897%2F145%29i Reduce.


So %28-9%2B2i%29%2F%28-8-9i%29=54%2F145-%2897%2F145%29i.


So the expression is now in standard form a%2Bbi where a=54%2F145 and b=-97%2F145