What does ((1+i)*(6-2i))/(4i) equal?

Oct 21, 2015

$1 - 2 i$

Explanation:

Given equation =$\frac{\left(1 + i\right) \left(6 - 2 i\right)}{4} i$

Expand the numerator

= $\frac{6 - 2 i + 6 i - 2 {i}^{2}}{4 i}$
= $\frac{6 + 4 i - 2 \left(- 1\right)}{4 i}$
= $\frac{6 + 4 i + 2}{4 i}$
= $\frac{8 + 4 i}{4 i}$
Take 4 as common in numerator
= $\frac{4 \left(2 + i\right)}{4 i}$
=$\frac{2 + i}{i}$
multiply numerator and denominator with $i$
= $\frac{2 i + {i}^{2}}{{i}^{2}}$
= $\frac{2 i - 1}{- 1}$
= $1 - 2 i$