AP EAMCET · Maths · Complex Number
\[
\mathrm{z}=\cos \theta+\mathrm{i} \sin \theta \Rightarrow z^r+(\bar{z})^r=
\]
- A \(\cos r \theta\)
- B \(2 \cos r \theta\)
- C \(\sin \mathrm{r} \theta\)
- D \(2 \sin \mathrm{r} \theta\)
Answer & Solution
Correct Answer
(B) \(2 \cos r \theta\)
Step-by-step Solution
Detailed explanation
We have \(\mathrm{Z}=\cos \theta+\mathrm{i} \sin \theta\) now \(Z^r=\cos (\mathrm{r} \theta)+\mathrm{i} \sin (\mathrm{r} \theta)\) and \((\mathrm{Z})^{\mathrm{r}}=\cos (\mathrm{r} \theta)-\mathrm{i} \sin (\mathrm{r} \theta)\)…
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