AP EAMCET · Maths · Complex Number
\(\operatorname{Arg}\left[\frac{(1+i \sqrt{3})(-\sqrt{3}-i)}{(1-i)(-i)}\right]=\)
- A \(\frac{5 \pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{2 \pi}{3}\)
- D \(\frac{-\pi}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } z=\left[\frac{(1+i \sqrt{3})(-\sqrt{3}-i)}{(1-i)(-i)}\right] \\ = & {\left[\frac{-\sqrt{3}-i-3 i+\sqrt{3}}{-i-1}\right]=\frac{4 i}{1+i} \times \frac{1-i}{1-i}=2+2 i } \end{aligned}\) \(\operatorname{Arg}(z)\) lies in \(I^{\text {st }}\) quadrant…
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