SOLUTION: I'm trying to solve the following problem, but get stuck half way through it, can you please help me? 16 + 4i divided by 16 - 4i I've been trying the following, I tried multipl

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I'm trying to solve the following problem, but get stuck half way through it, can you please help me? 16 + 4i divided by 16 - 4i I've been trying the following, I tried multipl      Log On


   

Question 195529: I'm trying to solve the following problem, but get stuck half way through it, can you please help me?
16 + 4i divided by 16 - 4i
I've been trying the following, I tried multiply both the numerator and denominator by the conjugate of the denominator and this is as far as I get before getting stuck (16+4i) (16+4i) using the foil method I get 256 +64i+64i+16i^2. When I do the same for the denominator (16-4i)(16+4i) using the foil method I get 272. I combine the numerator and get the following 240+128i and then this is where I'm stuck I don't know what to do after this 240+128i/272. Can you please help me?
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%2816%2B4i%29%2F%2816-4i%29 Start with the given expression.


%28%2816%2B4i%29%2F%2816-4i%29%29%28%2816%2B4i%29%2F%2816%2B4i%29%29 Multiply the fraction by %2816%2B4i%29%2F%2816%2B4i%29.


%28%2816%2B4i%29%2816%2B4i%29%29%2F%28%2816-4i%29%2816%2B4i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%28256%2B64i%2B64i%2B16i%5E2%29%2F%28256%2B64i-64i-16i%5E2%29 Multiply.


%28240%2B128i%29%2F%28272%29 Combine like terms.


%28240%29%2F%28272%29%2B%28%28128%29%2F%28272%29%29i Break up the fraction.


15%2F17%2B%288%2F17%29i Reduce.


So %2816%2B4i%29%2F%2816-4i%29=15%2F17%2B%288%2F17%29i.


So the expression is now in standard form a%2Bbi where a=15%2F17 and b=8%2F17

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct so far, but you could simplify your answer some:
%28240%2B128i%29%2F272 Factor 16 from the numerator and the from the denominator.
cross%2816%29%2815%2B8i%29%2F%28cross%2816%29%2A17%29+=+highlight%28%2815%2B8i%29%2F17%29