Question:
If $a=1+i$, then $a^{2}$ equals
(a) 1 − i
(b) 2i
(c) (1 + i) (1 − i)
(d) i − 1
Solution:
(b) 2i
a = 1 + i
On squaring both the sides, we get,
$a^{2}=(1+i)^{2}$
$\Rightarrow a^{2}=1+i^{2}+2 i$
$\Rightarrow a^{2}=1-1+2 i \quad\left(\because i^{2}=-1\right)$
$\Rightarrow a^{2}=2 i$