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Trigonometry Section 11.4
Find the roots of complex numbers
Note: The cube root of 27 is the solution to the equation x3 = 27.
Theorem: Every complex number has n, nth roots.
Example: Find the cube roots of 8i.
Solve z3 = 8i
To find the nth roots a complex number a + bi
1. write equation zn = a + bi
(r cis Θ)3 = 8 cis 90o
2. write in polar form: (r cis θ)n = (s cisα)
3. apply DeMoivre’s Theorem rn cis nθ = s cis α
4. solve rn = s
and nθ = α finding n solutions
5. convert to rectangular form
Find the fourth roots of -16.
Find the square roots of 2 + 3i.
• Page 413
• Problems 2,4,6,10,15