Question: (a) Draw a picture of the complex plane with the complex solutions to z6 = 1 marked. (b) What is the exact formula (no trigonometric

(a) Draw a picture of the complex plane with the complex solutions to z6 = 1 marked.
(b) What is the exact formula (no trigonometric functions allowed) for the primitive sixth root of unity ζ6?
(c) Verify explicitly that
1 + ζ6 + ζ26 + ζ36 + ζ46 + ζ56 = 0.
(d) Give a geometrical explanation of this identity

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