SOLUTION: Simplify 5 _____

SOLUTION: Simplify 5 ______ 2 + 4i .

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

Multiply the fraction by .

Combine the fractions.

Distribute.

FOIL the denominator.

Multiply.

Replace {{i^2}}} with -1.

Multiply.

Combine like terms.

Break up the fraction.

Reduce.

So

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Answer by swincher4391(1107) (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
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