Q47 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics
Imaginary part of $\frac{(1-i)^3}{(2-i)(3-2 i)}$ is
- A$\frac{22}{65}$
- B$\frac{6}{65}$
- C$-\frac{6}{65}$
- Correct answerD$-\frac{22}{65}$
Solution
$Z=\frac{(1-i)^3}{(2-i)(3-2 i)}=\frac{(1-i)^3}{4-7 i} \times \frac{4+7 i}{4+7 i}$
$\Rightarrow Z=\frac{6-22 i}{65} \Rightarrow \operatorname{Img}(Z)=\frac{-22}{65}$
$\Rightarrow Z=\frac{6-22 i}{65} \Rightarrow \operatorname{Img}(Z)=\frac{-22}{65}$
Hence, the correct answer is option: 'D'.