Chapter 6.5, Problem 28E

To determine

To calculate:

Sum of given complex numbers geometrically.

Answer to Problem 28E

Sum of given complex numbers geometrically is $2+i$ shown as below:

  

Explanation of Solution

Given information:

Complex number $\left(3-i\right)\left(-1+2i\right)$

Calculation:

Consider given Complex number is $\left(3-i\right)\left(-1+2i\right)$

To find the sum of given complex number $\left(3-i\right)$ and $\left(-1+2i\right)$ first writes it as vector,

  $u=\langle 3,-1\rangle ,v=\langle -1,2\rangle$

Now represent vector $u,v$ and sum $u+v$ in the complex plane,

  

From the above graph, it is observed that sum of vector is,

  $u+v=2+i$

That implies,

  $\left(3-i\right)+\left(-1+2i\right)=2+i$

Therefore, the sum is $2+i$ .