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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers3 Marks
Question
If $\text{z}_1=2-\text{i}, \ \text{z}_2=-2+\text{i},$ Find
$\text{Im}\Big(\frac{1}{\text{z}_1\bar{\text{z}}_1}\Big)$
✓

Answer

$\frac{1}{\text{z}_1\bar{\text{z}}_1}=\frac{1}{|\text{z}|^2}$
$=\frac{1}{|2-\text{i}|^2}$
$=\frac{1}{2^2+(-1)^2}$
$=\frac{1}{4+1}$
$=\frac{1}{5},$ which is purely real
$\therefore \ \text{Im}\Big(\frac{1}{\text{z}_1\bar{\text{z}}_1}\Big)=0$

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