COMEDK · Maths · 3. Complex Number
The modulus and amplitude of \((1+i \sqrt{3})^{8}\) are respectively
- A 256 and \(\frac{8 \pi}{3}\)
- B 2 and \(\frac{2 \pi}{3}\)
- C 256 and \(\frac{2 \pi}{3}\)
- D 256 and \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(C) 256 and \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
Let \(z=(1+i \sqrt{3})^{8}\) \(=\left(2\left(\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)\right)^{8}\) \(=\left[2\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)\right]^{8}=\left(2^{8} e^{i \pi / 3}\right)^{8}\)…
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