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  3. a draw a picture of the 6th roots of unity...

Question: a draw a picture of the 6th roots of unity...

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a. Draw a picture of the 6th roots of unity in the complex plane. Label them ), and C, D, E, F going A, B, C, D, E, F with A = 1 , B = cis counterclockwise around the circle. b. Fill in each of the following blanks with the letter corresponding to the product of the two complex numbers. For example, c. Using your answers from part (b), on your picture draw an arrow from A to B . A, similarly draw arrows from B to B-B, C to B·C, and so on. What do you observe about the arrows? d. It appears that multiplying all of the corners of the hexagon ABCDEF by B produces a rotation of the hexagon. What is the angle of rotation? e. Fill in the blanks: E. A = 〈 1 〉 E. B = く2 〉 E. C 〈 3 〉 f. Just as in part (c), use your answers from part (d) to draw arrows from A to E . A, B to E , B, etc. What do you observe about the arrows? g. Fill in the blanks: If you choose one particular 6th root of unity and multiply it with all the other 6th roots, the new values correspond to different く1 〉 of the original hexagon. The angle of 〈 2 〉 is equal to the complex argument of the <3>

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