AP EAMCET · Maths · Complex Number
The number of all possible solutions of the equation \(\mathrm{z}^3+\overline{\mathrm{z}}=0\) is
- A 4
- B 5
- C 3
- D 6
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given that } z^3+\bar{z}=0 \Rightarrow z^3=-\bar{z} \\ & \Rightarrow|z|^3=|-\bar{z}|=|z| \Rightarrow|z|\left(|z|^2-1\right)=0 \\ & |z|=0 \text { or }|z|^2=1 \Rightarrow z \bar{z}=1 \Rightarrow \bar{z}=\frac{1}{z} \\ & \therefore z^3+\bar{z}=0…
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