Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

Write each complex number in the standard form a + bi and plot each in the complex plane.

$2(\cos {150}^o+i\sin {150}^o)$

Step-by-Step Solution

Answer

The complex number is $-\sqrt{3}+i$

Step 1. Find x coordinate

The x coordinate $2(\cos {150}^o+i\sin {150}^o)$ is,

$x=r\cos \theta$

$x=2\sin {150}^o$

$x=2(-\frac{\sqrt{3}}{2})$

$x=-\sqrt{3}$

Step 2. Find Y coordinate

$y=r\sin \theta$

$y=2\sin {150}^o$

$y=2\left(\frac{1}{2}\right)$

$y=1$

The complex number is $-\sqrt{3}+i$