AP EAMCET · Maths · Complex Number
Imaginary part of \(\frac{(1-i)^3}{(2-i)(3-2 i)}\) is
- A \(\frac{22}{65}\)
- B \(\frac{6}{65}\)
- C \(-\frac{6}{65}\)
- D \(-\frac{22}{65}\)
Answer & Solution
Correct Answer
(D) \(-\frac{22}{65}\)
Step-by-step Solution
Detailed explanation
\(Z=\frac{(1-i)^3}{(2-i)(3-2 i)}=\frac{(1-i)^3}{4-7 i} \times \frac{4+7 i}{4+7 i}\) \(\Rightarrow Z=\frac{6-22 i}{65} \Rightarrow \operatorname{Img}(Z)=\frac{-22}{65}\)
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