Chapter 6.5, Problem 31E

To determine

To calculate:

Sum of given complex numbers geometrically.

Answer to Problem 31E

Difference of given complex numbers geometrically is $-2-2i$ Shown as below:

  

Explanation of Solution

Given information:

Complex number $\left(4+2i\right)\left(6+4i\right)$

Calculation:

Consider given Complex number is $\left(4+2i\right)\left(6+4i\right)$

To find the difference of given complex number $\left(4+2i\right)$ and $\left(6+4i\right)$ first writes it as vector,

  $u=\langle 4,2\rangle ,v=\langle 6,4\rangle$

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,

  $u-v=-2-2i$

That implies,

  $\left(4+2i\right)-\left(6+4i\right)=-2-2i$

Therefore, the difference is $-2-2i$ .