AP EAMCET · Maths · Complex Number
If \(\mathrm{Z}=x+i y\) is a complex number, then the number of distinct solution of the equation \(z^3+\bar{z}=0\) is
- A \(1\)
- B \(3\)
- C Infinite
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
Given, \(z^3+\bar{z}=0\), where \(z=x+i y\) is a complex number \(\begin{aligned} & \Rightarrow z^3=-\bar{z} \Rightarrow\left|z^3\right|=|-\bar{z}| \Rightarrow|z|^3=|z| \\ & \Rightarrow|z|^3-|z|=0 \Rightarrow|z|\left(|z|^2-1\right)=0\end{aligned}\)…
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