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Find the complex number w that satisfies w³ = 8i and lies in the second quadrant of the complex plane.

1. -sqrt(3) + i
2. -sqrt(3)/2 + 1/2 i
3. -2sqrt(3) + i
4. -sqrt(3) + 2i

Correct answer: -sqrt(3) + i

Solution

Cube roots of 8i have modulus 2 and arguments 30, 150, 270 degrees. The root at 150 deg is 2(cos150 + i sin150) = -sqrt(3) + i, which lies in the second quadrant.

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