A complex number $z$ among the following which satisfy $z^3+27 i=0$ is

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Aicharya · Accepted Answer

Given, $z^3+27 i=0$ $\begin{aligned} & \Rightarrow \quad z^3-(3 i)^3=0 \ & \Rightarrow \quad(z-3 i)\left(z^2+3 z i-9ight)=0\end{aligned}$ If $\quad z-3 i=0 \Rightarrow z=3 i$ If $z^2+3 z i-9=0$ $\begin{aligned} & \Rightarrow \quad z=\frac{-3 i \pm \sqrt{-9+36}}{2}=\frac{-3 i \pm 3 \sqrt{3}}{2} \ & \Rightarrow \quad z=\frac{3 \sqrt{3}-3 i}{2}, \frac{-3 \sqrt{3}-3 i}{2}\end{aligned}$

A complex number $z$ among the following which satisfy $z^3+27 i=0$ is

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