The number of distinct complex number(s) z𝑧, such that |z|=1𝑧=1 and z3𝑧3 is purely imaginary, is/are equal to

Question

The number of distinct complex number(s) z𝑧, such that |z|=1𝑧=1 and z3𝑧3 is purely imaginary, is/are equal to
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Solution 1

The given conditions are |z| = 1 and z^3 is purely imaginary.

  1. The condition |z| = 1 means that z lies on the unit circle in the complex plane.

  2. The condition z^3 is purely imaginary means that z^3 can be written in the form 0 + yi, where y is a real number.

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