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If a complex number z satisfies z + 1/z = 2 cos 3deg, find the value of z²⁰⁰⁰ + 1/z²⁰⁰⁰ + 1.

1. 0
2. -1
3. sqrt(3) + 1
4. 1 - sqrt(3)

Correct answer: 0

Solution

Since 6000deg reduces to 240deg, cos(6000deg) = -1/2, making the sum 2(-1/2) + 1 = 0.

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