Question

Express 2i/1+i in the form a+bi, where

a,b∈R.

Answer 1

Multiply the numerator and denominator by $\overline{1+i}=1-i$:

$\frac{2i}{1+i}=\frac{2i(1-i)}{(1+i)(1-i)}=\frac{2i-2i^2}{1^2-i^2}=\frac{2i-2(-1)}{1-(-1)}=\frac{2i+2}{1+1}=\frac{2+2i}{2}=\frac{2}{2}+\frac{2i}{2}=1+i$.