TS EAMCET · Maths · Complex Number
In Argand plane, no value of \(\sqrt[3]{1-i \sqrt{3}}\) lie in
- A First quadrant
- B Second quadrant
- C Third quadrant
- D Fourth quadrant
Answer & Solution
Correct Answer
(A) First quadrant
Step-by-step Solution
Detailed explanation
\(z = 1 - i\sqrt{3} = 2\left(\cos\left(-\frac{\pi}{3}\right) + i \sin\left(-\frac{\pi}{3}\right)\right)\) The cube roots are \(z_k = \sqrt[3]{2} \left(\cos\left(\frac{-\frac{\pi}{3} + 2k\pi}{3}\right) + i \sin\left(\frac{-\frac{\pi}{3} + 2k\pi}{3}\right)\right)\) for…
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