Answer
$-i$
Work Step by Step
$i^{0}=1$
$i^{1}=i$
$i^{2}=-1$
$i^{3}=-i$
$i^{4}=1 ...$
---
$i^{43}=i^{40+3}=$
$=i^{40}\cdot i^{3}$
$=(i^{4})^{10}\cdot i^{3}$
$=1^{10}\cdot(-i)$
$=-i$
Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
by Bittinger, Marvin L.; Ellenbogen, David J.; Johnson, Barbara L.
Published by
Pearson
ISBN 10:
0-32184-874-8
ISBN 13:
978-0-32184-874-1
Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 788: 80
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