Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 111: 10

(c) fourth

$i^{1}=i$ $i^{2}=-1$ $i^{3}=i^{2}\cdot i=-1\cdot i=-i$ $i^{4} =i^{2}\cdot i^{2}=(-1)(-1)=1$ Since $i^{4}=1$, then $i^{8}=i^{12}=...=i^{4n}=1$, and $ i^{4n+1}=1\cdot i^{1}=i$ $ i^{4n+2}=1\cdot i^{2}=-1$ $ i^{4n+3}=1\cdot i^{3}=-i$ Every fourth power repeats.