The complex number i: If we define i = -1, show that i? = -1, i3 = -i, and i4 = 1. Euler's Formula: Use the results of the previous exercise and the Maclaurin series for the sine, the cosine, and the exponential function to derive Euler's formula e* = cos x +i sin x.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The complex number i: If we define i = -1, show that
i? = -1, i3 = -i, and i4 = 1.
Euler's Formula: Use the results of the previous exercise
and the Maclaurin series for the sine, the cosine, and
the exponential function to derive Euler's formula
e* = cos x +i sin x.
Transcribed Image Text:The complex number i: If we define i = -1, show that i? = -1, i3 = -i, and i4 = 1. Euler's Formula: Use the results of the previous exercise and the Maclaurin series for the sine, the cosine, and the exponential function to derive Euler's formula e* = cos x +i sin x.
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