Chapter 8.3, Problem 26E

To determine

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

Answer to Problem 26E

Graph for set of complex numbers is sketched on complex plane

Explanation of Solution

Given information: Set of complex numbers is $\left\{z=a+bi|2\le \left|z\right|\le 5\right\}$

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

  $\left\{z=a+bi|2\le \left|z\right|\le 5\right\}$

Here, set represents the complex numbers with modulus less than and equal to $5$ and greater than and equal to $2$

Thus,

  $\begin{array}{l}2\le \left|z\right|\le 5\\ 2\le \sqrt{a^2+b^2}\le 5\end{array}$

This is set of complex number such that all points are at least at a distance of $2$ units from the origin and at most at a distance of $5$ units from the origin.

Hence, the graph is a region enclosed by a disc defined by the boundaries of two circles, one of radius $5$ units and other of radius $2$ units

Here, shaded region represents the points that are included

  

Conclusion:

Hence, set of complex numbers are sketched