How do you simplify #(2+4i)/(2i)#?

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Answer 1 · 2016-09-10T02:39:43

#2-i#

First, rewrite the denominator in #a+bi# form

#(2+4i)/(0+2i)#

Secondly, multiply by the numerator and denominator by the complex conjugate of the denominator as follows:

#((2+4i)/(0+2i))((0-2i)/(0-2i))#

Expand numerator and denominator.

#(0-4i+0i-8i^2)/(0-0i+0i-4i^2)#

Recall that #i^2=-1#

#(-4i+8)/4=(-4i)/4+8/4=-i+2=2-i#