SOLUTION: Simplify quotient and write answer in a + bi form. 6 + 2i divided by 4-3i

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Question 195104: Simplify quotient and write answer in a + bi form.
6 + 2i divided by 4-3i
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%286%2B2i%29%2F%284-3i%29 Start with the given expression.


%28%286%2B2i%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%2B2i%29%284%2B3i%29%29%2F%28%284-3i%29%284%2B3i%29%29 Combine the fractions.


%28%286%29%284%29%2B%286%29%283i%29%2B%282i%29%284%29%2B%282i%29%283i%29%29%2F%28%284-3i%29%284%2B3i%29%29 FOIL the numerator.


%28%286%29%284%29%2B%286%29%283i%29%2B%282i%29%284%29%2B%282i%29%283i%29%29%2F%28%284%29%284%29%2B%284%29%283i%29%2B%28-3i%29%284%29%2B%28-3i%29%283i%29%29 FOIL the denominator.


%2824%2B18i%2B8i%2B6i%5E2%29%2F%2816%2B12i-12i-9i%5E2%29 Multiply.


%2818%2B26i%29%2F%2825%29 Combine like terms.


18%2F25%2B%2826%2F25%29i Break up the fraction.


So %286%2B2i%29%2F%284-3i%29=18%2F25%2B%2826%2F25%29i.


So the expression is now in standard form a%2Bbi where a=18%2F25 and b=26%2F25