If $z + z^3=0$ then which of the following must be true on the complex plane?

Question

A) $Re(z)<0$
B) $Re(z)=0$
C) $Im(z)=0$
D) $z^4=1$

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Answer 1 · 2018-03-01T14:01:40

From the given relation we have that

$z+z^3=0=>z(1+z^2)=0$

Hence $z=0$ and $1+z^2=0=>z=+-i$

So the correct answer is B $Re(z)=0$