Question

Select the correct answer.4cisConvert 3 to rectangular form.isrO A.-2 – 231O B.-2 + 2V3OC. 2 - 2/3:OD. 2 + 2/31

Answer 1

As per given by the question,

There are given that the trigonometric function,

$4\cos \frac{5\pi}{3}$

Now,

The general form of the rectangula form is,

$a+ib$

Now,

Written the given trigonometric in the form of complex,

So

$Z=4\lbrack\cos \frac{5\pi}{3}+i\sin \frac{5\pi}{3}\rbrack$

Then,

$\begin{gathered} z=4\lbrack\cos \frac{5\pi}{3}+i\sin \frac{5\pi}{3}\rbrack \\ z=4\lbrack\cos (300)+i\sin (300)\rbrack \end{gathered}$

Then,

$\begin{gathered} z=4\lbrack\cos (300)+\text{isin}(300)\rbrack \\ z=4\lbrack0.5+i(-0.866)\rbrack \\ z=2+i(-0.866\times4) \\ z=2-i3.46 \\ z=2-2\sqrt[]{3}i \end{gathered}$

Hence, the option c is correct.