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#