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Let z be a complex number satisfying z⁶ + z³ + 1 = 0. If a root can be written as r*e^(i*theta) with 90 deg < theta < 180 deg, find theta.

1. 100 deg
2. 110 deg
3. 160 deg
4. 170 deg

Correct answer: 160 deg

Solution

From z³ = e^(i*120 deg) or e^(i*240 deg), the arguments of z are multiples giving 40, 160, 280 deg and 80, 200, 320 deg; the one strictly between 90 and 180 deg is 160 deg.

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