Gujarat 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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