Question

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

• A. Re(z) < 0
• B. Re(z) = 0
• C. Im(z) = 0
• D. z⁴ = 1

Answer 1

The correct option is B

Re(z) = 0

z(1+$z^2$ ) = 0 $\Rightarrow$ z=0 or $z^2$ = $i^2$ $\Rightarrow$ z = 0 or z = ± i $\Rightarrow$ Re(z) = 0.