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 9E
To determine

To evaluate: The expression 11+i in the form of a+bi.

Expert Solution

Answer to Problem 9E

The value of the expression 11+i is 1212i.

Explanation of Solution

Obtain the complex conjugate of number 1+i.

Use the property of conjugates z+w¯=z¯+w¯ and zw¯=z¯w¯ to simplify the expression as follows.

1+i¯=1¯+i¯=1¯+i¯=1i[i¯=i]

Thus, the complex conjugate of the number 1+i is 1i.

Multiply numerator and denominator of the expression 11+i by the complex conjugate of the denominator 14i and simplify the expression as follows.

11+i=11+i(1i1i)=1i12(i)2=1i2[i2=1]=1212i

Thus, the value of the expression 11+i is 1212i.

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