MATH

Which expression is the is a fourth root of -1+i sqrt3
1. the fourth root of 2 (cos(280 degrees)+i sin(280 degrees))

2.the fourth root of 2 (cos(30 degrees)+i sin(30 degrees))

3.the fourth root of 2 (cos(60 degrees)+i sin(60 degrees))

4.the fourth root of 2 (cos(320 degrees)+i sin(320 degrees))

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  1. r e^iT = r cos T + i r sin T

    r cos T = -1
    r sin T = sqrt 3
    30, 60 90 triangle in second quadrant r = 2, T = 180-60 = 120
    so
    2e^120i

    foruth root is 2^.25 e^(120/4)i
    2^.25 e^30 i

    2^.25 ( cos 30 + i sin 30)

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