AP EAMCET · Maths · Complex Number
If \((x-i y)^{1 / 3}-a-i b\), then the value of \(\frac{x}{2 a}+\frac{y}{2 b}\) is
- A \(2\left(a^2-b^2\right)\)
- B \(4\left(a^2-b^2\right)\)
- C \(a^2-b^2\)
- D \(\frac{1}{2}\left(a^2-b^2\right)\)
Answer & Solution
Correct Answer
(A) \(2\left(a^2-b^2\right)\)
Step-by-step Solution
Detailed explanation
\((x-i y)^{1 / 3}=a-i b\) \((x-i y)=(a-i b)^3\) \(\begin{aligned} & =a^3-i^3 b^3-3 a^2(\mathrm{ib})+3 \mathrm{a}(\mathrm{ib})^2 \\ & =a^3+i b^3-3 a^2 b i-3 a b^2\end{aligned}\)…
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