AP EAMCET · Maths · Complex Number
If \(a=\operatorname{Im}\left(\frac{1+z^2}{2 i z}\right)\) and \(z\) is any non zero complex number such that \(|z|=1\), then
\(a=\)
- A \(\operatorname{Re}(z)\)
- B \(\operatorname{Re}(z) \operatorname{Im}(z)\)
- C \(-\operatorname{Re}(z)\)
- D \(\operatorname{Re}(z)+\operatorname{Im}(z)\)
Answer & Solution
Correct Answer
(C) \(-\operatorname{Re}(z)\)
Step-by-step Solution
Detailed explanation
\(a=\operatorname{Im}\left(\frac{1+z^2}{2 i z}\right)\) Given \(|z|=1 \implies \frac{1}{z}=\bar{z}\). \(a = \operatorname{Im}\left(\frac{1}{2i}\left(\frac{1}{z}+z\right)\right)\) \(a = \operatorname{Im}\left(\frac{1}{2i}(z+\bar{z})\right)\)…
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