# Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 92

$1$

#### Work Step by Step

RECALL: (1) $a^{mn} = (a^m)^n$ (2) $i^2=-1$ (3) $a^{m+n} = a^m \cdot a^n$ Use rule (1) above to obtain: $=(i^2)^{200}$ Use rule (2) to obtain: $=(-1)^{200}$ Note that when $-1$ raised to an even power, the result is $1$. Thus, $(-1)^{200} = 1$

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