Question 529806
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