# The complex conjugate and modulus of the number − 4 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 17E
To determine

## To find: The complex conjugate and modulus of the number −4i.

Expert Solution

The complex conjugate of the number 4i is 4i.

The modulus of the number 4i is 4.

### Explanation of Solution

Obtain the complex conjugate of number 4i.

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

4i¯=4¯(i¯)=4(i)[i¯=i]=4i

Thus, the complex conjugate of the number 4i is 4i.

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

Obtain the modulus of the number 4i.

|4i|=02+(4)2=0+16=16=4

Thus, the modulus of the number 4i is 4.

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