BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter I, Problem 46E
To determine

To write: The number eπ+i in the form a+bi.

Expert Solution

Answer to Problem 46E

The number eπ+i expressed in the form of complex number as eπcos1+(eπsin1)i.

Explanation of Solution

Formula used:

Euler’s formula:

eiy=cosy+isiny

Calculation:

Simplify the number eπ+i by using Euler’s formula as follows.

eπ+i=eπei=eπ(cos1+isin1)=eπcos1+(eπsin1)i

Thus, the number eπ+i expressed in the form of complex number as eπcos1+(eπsin1)i.

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