FINDING ROOTS OF COMPLEX NUMBERS USING DE MOIVRES THEOREM WORKSHEET

Problem 1 :

If Ī± and Ī² are the roots of x2 + x + 1 = 0, then Ī±2020 + Ī²2020 is

(1)   -2   (2)  -1    (3)    1   (4)   2

Solution

Problem 2 :

The product of all four values of cos šœ‹3 + i sin šœ‹334is

(1)   -2   (2)   -1    (3)   1    (4)  2

Solution

Problem 3 :

If Ļ‰ ā‰  1 is a cubic root of unity and 1111-Ļ‰2 - 1Ļ‰21Ļ‰2Ļ‰7 = 3k, then k is equal to

(1)   1    (2)  -1   (3)  āˆš3i    (4)   -āˆš3i

Solution

Problem 4 :

The value of 1 + 3i1 - 3i10is
(1) cis 2šœ‹3
(3) -cis 2šœ‹3
(2) cis 4šœ‹3
(4) -cis 4šœ‹3

Solution

Problem 5 :

If šœ” = cis 2šœ‹3, then the number of distinct roots of z + 1šœ”šœ”2šœ”z + Ļ‰2 1šœ”21z + Ļ‰ = 0

(1)  1   (2)   2   (3)   3   (4)   4

Solution

Answer Key

1) -1

2)  1

3)  -āˆš3 i

4) cis 2Ļ€/3

5)  0

Solve each equation in the complex number system. Express solutions in polar and rectangular form.

Problem 1 :

x5 - 32i = 0

Solution

Problem 2 :

x3 - (1 + iāˆš3) = 0

Solution

Problem 3 :

x3 - (1 - iāˆš3) = 0

Solution

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