a. Answer The complex conjugate of Explanation Given information :the statement is given as, The complex conjugate of 3 + 4 i is 3 + 4 i ¯ = _ _ The product of a complex number and its conjugate is always a non-negative real number. For the complex number 3 + 4 i , the complex conjugate be, 3 + 4 i ¯ = 3 − 4 i Therefore, The complex conjugate of 3 + 4 i is 3 + 4 i ¯ = 3 − 4 i . b. To determine To fill in the blank. Answer For the complex number 3 + 4 i the real part is 3 and the imaginary part is 4 . Explanation Given information :the statement is given as, ( 3 + 4 i ) ( 3 + 4 i ¯ ) = _ _ The product of a complex number and its conjugate is always a non-negative real number. The complex conjugate of 3 + 4 i is 3 + 4 i ¯ = 3 − 4 i . ( 3 + 4 i ) ( 3 + 4 i ¯ ) = ( 3 + 4 i ) ( 3 − 4 i ) = ( 9 − 16 i 2 ) + ( 12 i − 12 i ) = ( 9 + 16 ) = 25 Therefore, ( 3 + 4 i ) ( 3 + 4 i ¯ ) = 25

Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 3.5, Problem 3E

To determine

To fill in the blank.

Expert Solution

Answer to Problem 3E

The complex conjugate of

Explanation of Solution

Given information:the statement is given as,

The complex conjugate of 3+4i is 3+4i¯=__

The product of a complex number and its conjugate is always a non-negative real number.

For the complex number 3+4i , the complex conjugate be,

3+4i¯=3−4i

Therefore,

The complex conjugate of 3+4i is 3+4i¯=3−4i .

To determine

To fill in the blank.

Expert Solution

Answer to Problem 3E

For the complex number 3+4i the real part is 3 and the imaginary part is 4 .

Explanation of Solution

Given information:the statement is given as,

(3+4i)(3+4i¯)=__

The product of a complex number and its conjugate is always a non-negative real number.

The complex conjugate of 3+4i is 3+4i¯=3−4i .

(3+4i)(3+4i¯)=(3+4i)(3−4i)=(9−16i2)+(12i−12i)=(9+16)=25

Therefore,

(3+4i)(3+4i¯)=25

Chapter 3.5, Problem 2E

Chapter 3.5, Problem 4E

Chapter 3 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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