Russian Maths | Olympiad Maths | Math Simplification for X?

A Wonderful math olympiad question. How to solve math problem.
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-1+_i, 1+_i.

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x^(4) = - 4 ← as negative number → complex number to be used x^(4) = 4i² x^(4) = (± 2i)² x² = ± 2i x = a + ib → where: a ≠ 0 and where b ≠ 0 x² = (a + ib)² x² = a² + 2abi + i²b² x² = a² - b² + 2abi → recall: x² = ± 2i a² - b² + 2abi = ± 2i → by identification: a² - b² = 0 → a² = b² 2abi = ± 2i ab = ± 1 First case: a = 1 → b = ± 1 x = 1 + i ← this is the first root x = 1 - i ← this is the second root Second case: a = - 1 → b = ± 1 x = - 1 + i ← this is the third root x = - 1 - i ← this is the flourth root