SOLUTION: please help me simplify this expression into a+bi form 5+6i/4-2i

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Question 389787: please help me simplify this expression into a+bi form
5+6i/4-2i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2B6i%29%2F%284-2i%29 Start with the given expression.


%28%285%2B6i%29%2F%284-2i%29%29%28%284%2B2i%29%2F%284%2B2i%29%29 Multiply the fraction by %284%2B2i%29%2F%284%2B2i%29.


%28%285%2B6i%29%284%2B2i%29%29%2F%28%284-2i%29%284%2B2i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2820%2B10i%2B24i%2B12i%5E2%29%2F%2816%2B8i-8i-4i%5E2%29 Multiply.


%2820%2B10i%2B24i%2B12%28-1%29%29%2F%2816%2B8i-8i-4%28-1%29%29 Replace i%5E2 with -1.


%2820%2B10i%2B24i-12%29%2F%2816%2B8i-8i%2B4%29 Multiply.


%288%2B34i%29%2F%2820%29 Combine like terms.


%288%29%2F%2820%29%2B%28%2834%29%2F%2820%29%29i Break up the fraction.


2%2F5%2B%2817%2F10%29i Reduce.


So %285%2B6i%29%2F%284-2i%29=2%2F5%2B%2817%2F10%29i.


So the expression is now in standard form a%2Bbi where a=2%2F5 and b=17%2F10


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim