Question
If $\text{a}=1+\text{i},$ then a2 equals:
- $1-\text{i}$
- $2\text{i}$
- $(1+\text{i})(1-\text{i})$
- $\text{i}-1.$
Solution:
$\text{a}=1+\text{i}$
On squaring both the sides, we get,
$\text{a}^2=(1+\text{i})^2$
$\Rightarrow\text{a}^2=1+\text{i}^2+2\text{i}$
$\Rightarrow\text{a}^2=1-1+2\text{i} \ (\because\text{i}^2=-1)$
$\Rightarrow\text{a}^2=2\text{i}$
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