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Find the modulus and argument (amplitude) of the complex number -2 + 2*sqrt(3)*i.

1. modulus 4, argument 2pi/3
2. modulus 4, argument pi/3
3. modulus 2, argument 2pi/3
4. modulus 8, argument 5pi/6

Correct answer: modulus 4, argument 2pi/3

Solution

For -2 + 2sqrt3 i, modulus = sqrt(4 + 12) = 4 and the reference angle is arctan(2sqrt3/2) = pi/3, placing the argument at pi - pi/3 = 2pi/3.

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