- #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?

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- Thread starter Stripe
- Start date

In summary, the conversation is about simplifying the expression (2 CIS (pi/6))*(3 CIS (pi/12)) and converting it from polar form to Cartesian form using the notation "CIS" to represent cos+ i*sin. The solution involves using De Moivre's theorem and applying the definition of "CIS."

- #1

- 32

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

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

i simplified it to

6 CIS (pi/12)

How do i turn it into cartesian?

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- #2

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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))

(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:

- #3

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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].

A complex number is a number that has two parts: a real part and an imaginary part. The imaginary part is represented by the letter "i" and is equal to the square root of -1. A real number, on the other hand, only has one part and can be represented on a number line.

To simplify a complex number, you need to combine the real and imaginary parts. This is done by adding or subtracting the real and imaginary parts separately. For example, if you have the complex number 3 + 2i, you would simplify it to 3 + 2i. If you have the complex number 3 - 2i, you would simplify it to 3 - 2i.

The cartesian form of a complex number is when the real and imaginary parts are written as a pair in the form (a, b), where "a" is the real part and "b" is the imaginary part. This form is also known as the rectangular form.

To convert a complex number from polar form to cartesian form, you can use the following formula: z = r(cosθ + isinθ), where "r" is the modulus (or absolute value) and "θ" is the argument (or angle) of the complex number. Simply plug in the values for r and θ and simplify the expression to get the cartesian form.

Yes, a complex number can be represented graphically on a complex plane, also known as an Argand diagram. The real part of the complex number is represented on the horizontal axis, while the imaginary part is represented on the vertical axis. The point where the two axes intersect is the origin, and the complex number is represented by a point on the plane.

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