Chapter 14.4, Problem 2WE

To determine

To find: The plot of complex numbers $w,z,w+z\text{ and }w-z$ in the complex plane.

Answer to Problem 2WE

  

Explanation of Solution

Given information:

Two complex numbers are given as −

  $w=-2-3i\text{ and }z=-2+3i$ .

Concepts used: Addition and subtraction of two complex numbers.

If $w=x_1+i{y}_1\text{ and }z=x_2+i{y}_2$ then −

  $\begin{array}{l}w+z=\left(x_1+x_2\right)+i\left(y_1+y_2\right)\\ w-z=\left(x_1-x_2\right)+i\left(y_1-y_2\right)\end{array}$

Calculation:

Two complex numbers are given as −

  $\begin{array}{l}w=-2-3i\text{ and }z=-2+3i\\ \text{So, }w+z=\left(-2-2\right)+i\left(-3+3\right)\\ \Rightarrow w+z=-4\\ \text{And }w-z=\left(-2+2\right)+i\left(-3-3\right)\\ \Rightarrow w-z=-6i\end{array}$

Plotting these complex number on complex plane as below − \