Answer
$-1$
Work Step by Step
$i^{1002}$
The basic rules of $i$ go as follows:
$i^0 = 1$
$i^1 = i$
$i^2 = -1$
$i^3 = -i$
We know $1002=2\times501$
$i^{1002}=(i^{2})^{501}=(-1)^{501}=-1$
All numbers raised to an odd power conserves the sign.
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises - Page 64: 52
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