Write the complex number in rectangular form.

Write the complex number in rectangular form. 3cis52degrees ( round to 3 decimal places)

What does $\displaystyle \text{cis}(\theta)$ mean? What I mean, is use the definition, write it out, then use your calculator to evaluate the trig. functions.

Cis = Cos * i sin

No, $\displaystyle \text{cis}(\theta)\equiv\cos(\theta)+i\sin(\theta)$.

So how would you expand $\displaystyle 3\,\text{cis}\left(52^{\circ} \right)$ ?

Wouldn't it be 3*cos52 + 3 * i sin52?

Yes, that's right, now just use your calculator to approximate the rectangular components. Rectangular form is:

$\displaystyle a+bi$ where $\displaystyle a,b\in\mathbb{R}$ (i.e. $\displaystyle a$ and $\displaystyle b$ are real.)

Here we have:

$\displaystyle a=3\cos\left(52^{\circ} \right)$

$\displaystyle b=3\sin\left(52^{\circ} \right)$

I got 1.847+2.364i as my answer, is that right?

Yes, that's correct! Good work! :D

Thank you! :D