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 (r cis Θ)3 = 8 cis 90o To find the nth roots a complex number a + bi 1. write equation zn = a + bi 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.

assignment Page 413 Problems 2,4,6,10,15