TS EAMCET · Maths · Complex Number
Number of real values of \((-1-\sqrt{3} i)^{3 / 4}\) is
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(z = -1 - \sqrt{3}i\) \(r = \sqrt{(-1)^2 + (-\sqrt{3})^2} = 2\) \(\theta = \arctan\left(\frac{-\sqrt{3}}{-1}\right) + \pi = \frac{\pi}{3} + \pi = \frac{4\pi}{3}\) \(z = 2\left(\cos\left(\frac{4\pi}{3}\right) + i\sin\left(\frac{4\pi}{3}\right)\right)\)…
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