# Simplifying and then expressing complex numbers in cartesian form

1. Mar 11, 2010

### Stripe

1. The problem statement, all variables and given/known data
(2 CIS (pi/6))*(3 CIS (pi/12))

2. Relevant equations

Also what is CIS? I believe it's Cos+i*sin but how do you use it?

3. The attempt at a solution
i simplified it to

6 CIS (pi/12)

How do i turn it into cartesian?

2. Mar 11, 2010

### tiny-tim

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

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

(and no, it's not 6 CIS (π/12))

Last edited: Mar 11, 2010
3. Mar 11, 2010

### HallsofIvy

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

The important thing about that notation is that $(Cis(\theta)*Cis(\phi)= Cis(\theta+ \phi)$.

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

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