Chapter 14.4, Problem 37WE

To determine

To show: The shaded triangles in the given diagram are similar.

Explanation of Solution

Given information:

Below diagram is given representing complex numbers.

  

Calculation:

Let us first label the given diagrams of complex number.

  

In above diagram, there are two triangles $OAB$ and $OCD$ .

  $\angle AOB=\angle COD$ ,

  $\frac{OA}{OD}=\frac{OB}{OC}=\left|z\right|$

Thus two sides are proportional and one angle is equal. This satisfies the condition for similar triangles.

Hence, $\Delta OAB\sim \Delta ODC$ .