TS EAMCET · Maths · Complex Number
The sum of the least positive arguments of the distinct cube roots of the complex number \((1-i \sqrt{3})\) is
- A \(\frac{5 \pi}{3}\)
- B \(\frac{17 \pi}{3}\)
- C \(\frac{23 \pi}{3}\)
- D \(\frac{11 \pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{11 \pi}{3}\)
Step-by-step Solution
Detailed explanation
Let \(z=1-i \sqrt{3}\) positive argument of \(z\) is \(2 \pi-\frac{\pi}{3}=\frac{5 \pi}{3}\) \[ \therefore \quad z=\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right) \] Cube root of \(z\) is…
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