Chapter 8.3, Problem 10E

To determine

To calculate: To graph the complex number and find its modulus

Answer to Problem 10E

Modulus of complex number is $\sqrt{58}$

Explanation of Solution

Given information: Complex number is $z=7-3i$

Formula Used:

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

  $z=a+bi$

Modulus of complex number $z=a+bi$ is defined

  $\left|z\right|=\sqrt{a^2+b}$

Calculation:

Complex number is given as

  $z=7-3i$

  $z=7+\left(-3\right)i$

On comparing with $z=a+bi$ ,

  $\begin{array}{l}a=7\\ b=-3\end{array}$

In order to graph the complex number, plot $\left(7,-3\right)$ on the x-y plane

  

Modulus of complex number is calculated as

  $\left|z\right|=\sqrt{a^2+b}$

Substituting the values,

  $\begin{array}{l}\left|z\right|=\sqrt{\left(7\right)+{\left(-3\right)}^2}\\ \left|z\right|=\sqrt{49+9}\\ \left|z\right|=\sqrt{58}\end{array}$

Conclusion:

Hence, modulus of complex number is $\sqrt{58}$