# The complex conjugate and modulus of the number − 1 + 2 2 i .

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter I, Problem 16E
To determine

## To find: The complex conjugate and modulus of the number −1+22i.

Expert Solution

The complex conjugate of the number 1+22i is 122i.

The modulus of the number 1+22i is 3.

### Explanation of Solution

Obtain the complex conjugate of number 1+22i.

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

1+22i¯=1¯+22i¯=1¯+(22¯(i¯))=122i[i¯=i]

Thus, the complex conjugate of the number 1+22i is 122i.

The modulus of a complex number z=a+ib is |z|=a2+b2.

From the above definition, obtain the modulus of the number 1+22i.

|1+22i|=(1)2+(22)2=1+8=9=3

Thus, the modulus of the number 1+22i is 3.

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