# Simplifying and then expressing complex numbers in cartesian form

• Stripe
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."

## 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?

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:
"$Cis(\theta)$" 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: $6 Cis(\pi/4)= 6 cos(\pi/4)+ 6i sin(\pi/4)$.

## 1. What is the difference between a complex number and a real number?

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.

## 2. How do you simplify a complex number?

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.

## 3. What is the cartesian form of a complex number?

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.

## 4. How do you convert a complex number from polar form to cartesian 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.

## 5. Can a complex number be represented graphically?

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.