SOLUTION: Please help me solve this equation: 2+6i \ 3-3i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please help me solve this equation: 2+6i \ 3-3i      Log On


   

Question 297082: Please help me solve this equation: 2+6i \ 3-3i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282%2B6i%29%2F%283-3i%29 Start with the given expression.


%28%282%2B6i%29%2F%283-3i%29%29%28%283%2B3i%29%2F%283%2B3i%29%29 Multiply the fraction by %283%2B3i%29%2F%283%2B3i%29.


%28%282%2B6i%29%283%2B3i%29%29%2F%28%283-3i%29%283%2B3i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%286%2B6i%2B18i%2B18i%5E2%29%2F%289%2B9i-9i-9i%5E2%29 Multiply.


%286%2B6i%2B18i%2B18%28-1%29%29%2F%289%2B9i-9i-9%28-1%29%29 Replace i%5E2 with -1.


%286%2B6i%2B18i-18%29%2F%289%2B9i-9i%2B9%29 Multiply.


%28-12%2B24i%29%2F%2818%29 Combine like terms.


%28-12%29%2F%2818%29%2B%28%2824%29%2F%2818%29%29i Break up the fraction.


-2%2F3%2B%284%2F3%29i Reduce.


So %282%2B6i%29%2F%283-3i%29=-2%2F3%2B%284%2F3%29i which is now in a%2Bbi form where a=-2%2F3 and b=4%2F3.