AP EAMCET · Maths · Complex Number
If \(z=1+i \sqrt{3}\) then \(|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|\) is equal to
- A 0
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{2 \pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(z=1+i \sqrt{3}\) Let \(1+i \sqrt{3}=r(\cos \theta+i \sin \theta)\) Then, \(\quad r \cos \theta=1\) \(\ldots\) (i) \(r \sin \theta=\sqrt{3}\) \(\ldots\) (ii) Eq. (i) + Eq. (ii), we get \(r^2\left(\sin ^2 \theta+\cos ^2 \theta\right)=3+1\)…
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