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Questions  

The equation  z3=z¯ has 

a
no solution
b
two solutions
c
five solutions
d
infinite number of solutions

detailed solution

Correct option is C

z3=z¯⇒z3=|z¯|⇒z3=|z¯|⇒|z|=0 or |z|=1⇒z=0 or z¯=1/z.∴z3=z¯⇒z3=1z⇒z4=1⇒z=1,−1,i,−i.Thus, solutions of  z3 = z  are  0, 1, –1, i, –i

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