Chapter 8.3, Problem 25E

To determine

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

Answer to Problem 25E

Graph for set of complex numbers is sketched on complex plane

Explanation of Solution

Given information: Set of complex numbers is $\left\{z=a+bi|\left|z\right|<2\right\}$

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

  $\left\{z=a+bi|\left|z\right|<2\right\}$

Here, set represents the complex numbers with modulus less than $2$

Thus,

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

This is set of complex number such that all points are no more than a distance of $2$ units away from the origin.

Hence, the graph is a region enclosed by a circle of radius $2$ centered at origin on complex plane

Here, shaded region represents the points that are included and dotted line represents that points on line are not included

  

Conclusion:

Hence, set of complex numbers are sketched