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Simplifying and then expressing complex numbers in cartesian form

  • Thread starter Stripe
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  • #1
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Homework Statement


(2 CIS (pi/6))*(3 CIS (pi/12))

Homework Equations



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


The Attempt at a Solution


i simplified it to

6 CIS (pi/12)

How do i turn it into cartesian?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi Stripe! :smile:

(have a pi: π :wink:)

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 :wink:

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:
  • #3
HallsofIvy
Science Advisor
Homework Helper
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"[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].
 

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