De Moivre's Theorem allows one to find powers of complex numbers in polar form and can be used for rational values of n, including integers and fractions. The document provides examples of using De Moivre's Theorem to find powers and roots of complex numbers expressed in rectangular and polar form. Students are assigned exercises to find specific powers of complex numbers using De Moivre's Theorem and expressing the results in rectangular form.

1. Precalculus
9-8 Powers and Roots of Complex Numbers
De Moivre’s Theorem:
6
EX1: Find ( 2 + 2 3ι) .
First write 2 + 2 3ι in polar form.
De Moivre’s Theorem is valid for all rational values of n, which includes
_________________________________________ and _______________________.
−5
 3 1 
EX2: Find  − ι .
 2 2 
EX3: Find 3
8i .

2. Classwork (turn in on a separate sheet of paper):
Find each power. Express the result in rectangular form.
3
  π π
1.  3  cos 6 + ι σ 6  
ιν
  
4
2. (1 + 3ι)
−2
3. ( 2 + 3ι)
4. 4
2 + 6ι