Chapter 6.5, Problem 30E

To determine

To calculate:

The sum of complex number geometrically.

Answer to Problem 30E

The sum of complex number geometrically is $3+i$ .

Explanation of Solution

Given information:

Complex number:

  $2i+\left(3-i\right)$

Formula used:

  $\left(a+bi\right)\pm \left(c+di\right)=\left(a\pm c\right)+\left(b\mp d\right)i$

Calculation:

Consider the $2i+\left(3-i\right)$

Group of the real part and the imaginary part of the complex number

  $\begin{array}{l}\left(a+bi\right)\pm \left(c+di\right)=\left(a\pm c\right)+\left(b\mp d\right)i\\ =\left(3\right)+\left(2-1\right)i\\ =3+i\end{array}$

The sum of complex number is $3+i$ .

The below graph shows the sum of complex number.