Chapter 8.3, Problem 18E

To determine

To calculate: To sketch the complex number $z$ and its complex conjugate on the same complex plane

Answer to Problem 18E

Complex number and its complex conjugate are sketched on complex plane

Explanation of Solution

Given information: Complex number is $z=-5+6i$

Formula Used:

Complex number is a number that can be expressed in the form of $a+bi$ , where $a$ and $b$ are real numbers

  $z=a+bi$

Conjugate of a complex number $z=a+bi$ is given as

  $\overline{z}=a-bi$

Calculation:

Complex number is given as

  $z=-5+6i$

Conjugate of above complex number is

  $\overline{z}=-5-6i$

On comparing the above complex numbers with standard form $z=a+bi$ ,

For complex number $z=-5+6i$

  $\begin{array}{l}a=-5\\ b=6\end{array}$

For complex number $\overline{z}=-5-6i$

  $\begin{array}{l}a=-5\\ b=-6\end{array}$

In order to graph the complex number, plot $\left(-5,6\right)$ and $\left(-5,-6\right)$ on the complex plane

  

Conclusion:

Hence, complex number and its complex conjugate are sketched