# If a = 1 + i, then

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

= 1 + i

On squaring both the sides, we get,

$a^{2}=(1+i)^{2}$

$\Rightarrow a^{2}=1+i^{2}+2 i$

$\Rightarrow a^{2}=1-1+2 i \quad\left(\because i^{2}=-1\right)$

$\Rightarrow a^{2}=2 i$

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