The equation z3=z¯ has

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no solution

two solutions

five solutions

infinite number of solutions

answer is C.

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Detailed Solution

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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