AP EAMCET · Maths · Complex Number
A complex number \(z\) among the following which satisfy \(z^3+27 i=0\) is
- A \((3 \sqrt{3}-3 i) / 2\)
- B \(-3 i\)
- C \((3 \sqrt{3}+3 i) / 2\)
- D \((-3 \sqrt{3}+3 i) / 2\)
Answer & Solution
Correct Answer
(A) \((3 \sqrt{3}-3 i) / 2\)
Step-by-step Solution
Detailed explanation
Given, \(z^3+27 i=0\) \(\begin{aligned} & \Rightarrow \quad z^3-(3 i)^3=0 \\ & \Rightarrow \quad(z-3 i)\left(z^2+3 z i-9\right)=0\end{aligned}\) If \(\quad z-3 i=0 \Rightarrow z=3 i\) If \(z^2+3 z i-9=0\)…
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