If a=1+i, then a2 equals: - Vidyadip

MCQ

If $\text{a}=1+\text{i},$ then a² equals:

A
$1-\text{i}$
B
$2\text{i}$
C
$(1+\text{i})(1-\text{i})$
D
$\text{i}-1.$

✓

Answer

$2\text{i}$

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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