SOLUTION: divide 7+4i --------- 9-5i

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Question 599387: divide
7+4i
---------
9-5i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%287%2B4i%29%2F%289-5i%29 Start with the given expression.


%28%287%2B4i%29%2F%289-5i%29%29%28%289%2B5i%29%2F%289%2B5i%29%29 Multiply the fraction by %289%2B5i%29%2F%289%2B5i%29.


%28%287%2B4i%29%289%2B5i%29%29%2F%28%289-5i%29%289%2B5i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2863%2B35i%2B36i%2B20i%5E2%29%2F%2881%2B45i-45i-25i%5E2%29 Multiply.


%2863%2B35i%2B36i%2B20i%5E2%29%2F%2881%2B45i-45i-25%28-1%29%29 Replace i%5E2 with -1.


%2863%2B35i%2B36i%2B20i%5E2%29%2F%2881%2B45i-45i%2B25%29 Multiply.


%2843%2B71i%29%2F%28106%29 Combine like terms.


43%2F106%2B%2871%2F106%29i Break up the fraction.


So %287%2B4i%29%2F%289-5i%29=43%2F106%2B%2871%2F106%29i.


So the expression is now in standard form a%2Bbi where a=43%2F106 and b=71%2F106