Simplifying and then expressing complex numbers in cartesian form

Hi Stripe!

(have a pi: π )

I've never seen "CIS" before, but I'll guess you're right, and that it's cos + i*sin.

Now use De Moivre's theorem … cosθ + isinθ = e^iθ

And Cartesian form simply means in the form x + iy (as opposed to polar form, which is in the form re^iθ )

(and no, it's not 6 CIS (π/12))

 

"[itex]Cis(\theta)[/itex]" is engineering notation for "[itex]cos(\theta)+ i sin(\theta)[/itex]" which mathematicians tend to write as [itex]e^{i\theta}[/itex].

The important thing about that notation is that [itex](Cis(\theta)*Cis(\phi)= Cis(\theta+ \phi)[/itex].

So you have correctly deduced that [itex](2Cis(\pi/6))(3Cis(\pi/12)= 6 Cis(3\pi/12)= 6 Cis(\pi/4)[/itex]

Now, just use the definition: [itex]6 Cis(\pi/4)= 6 cos(\pi/4)+ 6i sin(\pi/4)[/itex].