# Meredith's question at Yahoo! Answers regarding converting from trigonometric to rectangular form

Staff member

#### MarkFL

Staff member
Hello Meredith,

We are given:

$$\displaystyle z=7\sqrt{5}\text{cis}\left(\tan^{-1}(2) \right)=7\sqrt{5}\left(\cos\left(\tan^{-1}(2) \right)+i\sin\left(\tan^{-1}(2) \right) \right)$$

In order to evaluate the trig functions, consider the following diagram:

As you can see:

$$\displaystyle \tan(\theta)=\frac{2}{1}=2\,\therefore\,\theta= \tan^{-1}(2)$$

and so:

$$\displaystyle \sin(\theta)=\frac{2}{\sqrt{5}}$$

$$\displaystyle \cos(\theta)=\frac{1}{\sqrt{5}}$$

and so we have:

$$\displaystyle z=7\sqrt{5}\left(\frac{1}{\sqrt{5}}+i\frac{2}{ \sqrt{5}} \right)=7+14i$$

Hence:

$$\displaystyle a=7,\,b=14$$

To Meredith and any other guests viewing this topic, I invite and encourage you to post other complex number problems in our Pre-Calculus forum.

Best Regards,

Mark.