If $Z
eq 0$ is a complex number such that $Z^2+Z|Z|+|Z|^2=0$ then $Z$ is in the set (Here $\omega$ is a complex cube root of unity)

Question

If $Z 
eq 0$ is a complex number such that $Z^2+Z|Z|+|Z|^2=0$ then $Z$ is in the set (Here $\omega$ is a complex cube root of unity)

Aicharya · Accepted Answer

No solution. Refer to answer key.

If $Z \neq 0$ is a complex number such that $Z^2+Z|Z|+|Z|^2=0$ then $Z$ is in the set (Here $\omega$ is a…