Chapter 8.3, Problem 23E

To determine

To calculate: To sketch the set of complex numbers on the same complex plane

Answer to Problem 23E

Graph for set of complex numbers is sketched on complex plane

Explanation of Solution

Given information: Set of complex numbers is $\left\{z=a+bi|\left|z\right|=3\right\}$

Formula Used:

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

  $z=a+bi$

Calculation:

Set of complex numbers is given as

  $\left\{z=a+bi|\left|z\right|=3\right\}$

Here, set represents the complex numbers with modulus equal to $3$

Thus,

  $\begin{array}{l}\left|z\right|=3\\ \sqrt{a^2+b^2}=3\end{array}$

This is set of complex number such that all points are at a distance of $3$ units away from the origin.

Hence, the graph is a circle of radius $3$ on complex plane

Here, line represents that the points are included.

  

Conclusion:

Hence, set of complex numbers are sketched