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 $i^2=-1$

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

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