5.2.3 Operations with Complex Numbers (continued) Example 6 Evaluating Powers of i The first four powers of i are shown below. • i 1 = i
• i 2 = − 1 • i 3 = − i • i 4 = 1
These powers can be used to simplify higher powers of i , and express any power of i as either i , − 1, − i , or 1. Recall that expressions in simplest form cannot contain square roots in the denominator. Because the imaginary unit represents a square root, any denominator containing an imaginary unit (or complex number) must be rationalized. To rationalize the denominator in this case, multiply the numerator and denominator by the complex conjugate of the denominator.
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