FINDING ROOTS OF COMPLEX NUMBERS USING DE MOIVRES THEOREM WORKSHEET

Problem 1 :

If α and β are the roots of x² + x + 1 = 0, then α²⁰²⁰ + β²⁰²⁰ is

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

Solution

Problem 2 :

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

Solution

Problem 3 :

(1)   1    (2)  -1   (3)  √3i    (4)   -√3i

Solution

Problem 4 :

Solution

Problem 5 :

(1)  1   (2)   2   (3)   3   (4)   4

Solution

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 + i√3) = 0

Solution

Problem 3 :

x³ - (1 - i√3) = 0

Solution