Chapter 6.5, Problem 38E

To determine

To plot and find the complex conjugate of the complex number $5-4i$ .

Answer to Problem 38E

  $5+4i$

Explanation of Solution

Given:

Given complex number: $5-4i$

Concept used:

The complex conjugate a complex number $a+bi$ is $a-bi$ .

  $\overline{a+bi}=a-bi$

Calculation:

1. Plotting the given complex number:

  $\Rightarrow 5-4i$

Writing the above complex number in coordinate form,

  $\Rightarrow (5,-4)$

Graph:

  

2. Calculation of conjugate complex:

By using above concept, the conjugate complex of given complex number is,

  $\begin{array}{l}\overline{5-4i}=\overline{5+(-4)i}\\ =5-(-4)i\\ =5+4i\end{array}$

Conclusion:

Therefore, the conjugate complex of given complex number is $5+4i$ .