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Each of the complex numbers 1 + i*sqrt(3), -1 + i*sqrt(3), 1 - i*sqrt(3) and -1 - i*sqrt(3) has the same modulus 2. Which one of them has principal argument equal to 2*pi/3?

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

Correct answer: -1 + i*sqrt(3)

Solution

A complex number with argument 2*pi/3 lies in the second quadrant, so its real part is negative and its imaginary part is positive, which matches -1 + i*sqrt(3).

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