AP EAMCET · Maths · Complex Number
All the values of \((8 i)^{\frac{1}{3}}\) are
- A \(\pm(\sqrt{3}+i),-2 i\)
- B \(\pm \sqrt{3}+i,-2 i\)
- C \(\pm \sqrt{3}-i,-2 i\)
- D \(\pm(2+i), i\)
Answer & Solution
Correct Answer
(B) \(\pm \sqrt{3}+i,-2 i\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (8 i)^{1 / 3}=\left(-8 i^3\right)^{1 / 3}=-2 i \\ & i=e^{i \frac{\pi}{2}}=e^{i \frac{5 \pi}{2}} \end{aligned}\) \((8 i)^{1 / 3}=2 e^{\frac{i \pi}{6}}=2\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)=\sqrt{3}+i\)…
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