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Complex Numbers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers1 Mark
MCQ
If $\text{a}=1+\text{i},$ then $a^2$ equals:
  • A
    $1-\text{i}$
  • ✓
    $2\text{i}$
  • C
    $(1+\text{i})(1-\text{i})$
  • D
    $\text{i}-1.$
✓

Answer

Correct option: B.
$2\text{i}$
  1. $2\text{i}$
​​​​​​​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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