JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z\) is a non-real complex number, then the minimum value of \(\frac{{\operatorname{l} m{z^5}}}{{{{\left( {lmz} \right)}^5}}}\) is
- A \(-1\)
- B \(-4\)
- C \(-2\)
- D \(-5\)
Answer & Solution
Correct Answer
(B) \(-4\)
Step-by-step Solution
Detailed explanation
Let \(z=r e^{i \theta}\) Consider \(\frac{{\operatorname{Im} {z^5}}}{{{{(\operatorname{lm} z)}^5}}} \) \(= \,\frac{{{r^5}\,(\sin 5\theta )}}{{{r^5}\,{{(\sin \theta )}^5}}}\) \(\left(\because e^{i \theta}=\cos \theta+i \sin \theta\right)\)…
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