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How many solutions of the equation z³ + i*z - 1 = 0 are either real or purely imaginary?

1. zero
2. one
3. two
4. three

Correct answer: zero

Solution

Substituting a real z gives contradictory conditions (x = 0 and x³ = 1), and substituting a purely imaginary z also yields no consistent solution, so there are zero such roots.

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