Chapter 8.3, Problem 24E

To determine

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

Answer to Problem 24E

Graph for set of complex numbers is sketched on complex plane

Explanation of Solution

Given information: Set of complex numbers is $\left\{z=a+bi|\left|z\right|\ge 1\right\}$

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

  $\left\{z=a+bi|\left|z\right|\ge 1\right\}$

Here, set represents the complex numbers with modulus greater than and equal to $1$

Thus,

  $\begin{array}{l}\left|z\right|\ge 1\\ \sqrt{a^2+b^2}\ge 1\end{array}$

This is set of complex number such that all points are at least a distance of $1$ unit away from the origin.

Hence, the graph is a circle of radius $1$ centered at origin acting as a boundary on complex plane

Here, line and shaded region represents the points that are included.

  

Conclusion:

Hence, set of complex numbers are sketched