SOLUTION: Simplify 5 ______ 2 + 4i .

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Question 529806: Simplify 5
______
2 + 4i .
Found 2 solutions by jim_thompson5910, swincher4391:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285%29%2F%282%2B4i%29 Start with the given expression.


%28%285%29%2F%282%2B4i%29%29%28%282-4i%29%2F%282-4i%29%29 Multiply the fraction by %282-4i%29%2F%282-4i%29.


%28%285%29%282-4i%29%29%2F%28%282%2B4i%29%282-4i%29%29 Combine the fractions.


%2810-20i%29%2F%28%282%2B4i%29%282-4i%29%29 Distribute.


%2810-20i%29%2F%28%282%29%282%29%2B%282%29%28-4i%29%2B%284i%29%282%29%2B%284i%29%28-4i%29%29 FOIL the denominator.


%2810-20i%29%2F%284-8i%2B8i-16i%5E2%29 Multiply.


%2810-20i%29%2F%284-8i%2B8i-16%28-1%29%29 Replace {{i^2}}} with -1.


%2810-20i%29%2F%284-8i%2B8i%2B16%29 Multiply.


%2810-20i%29%2F%2820%29 Combine like terms.


%2810%29%2F%2820%29%2B%28%28-20%29%2F%2820%29%29i Break up the fraction.


1%2F2-i Reduce.


So %285%29%2F%282%2B4i%29=1%2F2-i


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Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
What you want to do is multiply by conjugate/conjugate of your complex number (2+4i). The conjugate of (2+4i) is (2-4i). What will happen is really nice. Your denominator will become a real number due to the fact that you are going to get a difference of two squares, and since i^2 = -1, you'll just end up with a real number. Watch and see.
(5/(2+4i)) * (2-4i)/(2-4i)
The numerator: 5*(2-4i) = 10 - 20i
The denominator: (2+4i)(2-4i)
Foil.
=4 - 8i + 8i -16i^2
=4 + 16 = 20 A REAL NUMBER!
So we have (10-20i)/20
Factor out a 10 out of the numerator.
(10(1-2i))/20
Divide through by 10 to get:
(1-2i)/2 <----- Answer