Cis (mathematics)

Cis is a special fancy word that math people use to talk about something called complex numbers, which are like regular numbers but with imaginary parts.

Now, when we talk about complex numbers, we can use different ways to describe them. One way is to use something called 'polar form', which is like giving the coordinates of a point on a map in terms of its distance from a center and the angle it makes with a certain line.

In polar form, a complex number is written as a distance from the center point (which is called the origin) and an angle measurement. And this is where the word cis comes in!

'Cis' is actually short for 'cosine + i sine', which means that we use the cosine of the angle and the sine of the angle to describe the complex number's imaginary and real parts. (i is just a special letter that stands for the imaginary unit, like how we use x or y for regular numbers).

So, if we have a complex number like 3 + 4i in polar form, we can write it as 5cis(arctan(4/3)) which means it's a distance of 5 from the origin and makes an angle of arctan(4/3) with the real line.

And that's what the word cis means in math! It's just a shorthand way to write complex numbers using their distance and angle measurements in a fancy way.