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 45E
To determine

To write: The number e2+iπ in the form a+bi.

Expert Solution

Answer to Problem 45E

The number e2+iπ expressed in the form of complex number as e2.

Explanation of Solution

Formula used:

Euler’s formula:

eiy=cosy+isiny

Calculation:

Simplify the number e2+iπ by the use of Euler’s formula as follows.

e2+iπ=e2eiπ=e2(cosπ+isinπ)=e2(1+i(0))=e2

Thus, the number e2+iπ expressed in the form of complex number as e2.

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