Mathematics - Complex Number Question with Solution | TestHub

(P) $z^3+z=0\Rightarrow z=0,i,-i$ $\Rightarrow \arg z=\pi /2$ or $-\pi /2$

(Q) $\left({\mathrm{z}}^3-1\right)\left({\mathrm{z}}^2+1\right)=0\Rightarrow \mathrm{z}=1,\mathrm{w},{\mathrm{w}}^2,\mathrm{i},-\mathrm{i}$ $\Rightarrow \arg z=0,\frac{2\pi }{3},-\frac{2\pi }{3},\frac{\pi }{2},-\frac{\pi }{2}$

(R) $(\mathrm{z}+1)\left({\mathrm{z}}^2+\mathrm{z}+1\right)=0\Rightarrow \mathrm{z}=-1,\mathrm{w},{\mathrm{w}}^2$ $\Rightarrow \arg z=-\frac{2\pi }{3},\frac{2\pi }{3},\pi$ ]

(S) Taking modules $|z{|}^2=|z|\Rightarrow |z|=0$ or $|z|=1$ $\Rightarrow \mathrm{z}=0\Rightarrow \mathrm{z}=\pm 1\Rightarrow \arg \mathrm{z}=0,\pi$