# The complex conjugate and modulus of the number 12 − 5 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 15E
To determine

## To find: The complex conjugate and modulus of the number 12−5i.

Expert Solution

The complex conjugate of the number 125i is 12+5i.

The modulus of the number 125i is 13.

### Explanation of Solution

Obtain the complex conjugate of number 125i.

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

125i¯=12¯5i¯=12¯(5¯(i¯))=12+5i[i¯=i]

Thus, the complex conjugate of the number 125i is 12+5i.

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

Obtain the modulus of the number 125i.

|125i|=122+(5)2=144+25=169=13

Thus, the modulus of the number 125i is 13.

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