Derivative of a Quadratic Function: Understanding the Use of cis(x)

[GreenPrint]

Homework Statement

Hi,

My teacher marked me wrong when I was asked to find the derivative of
-x^2 - 2x + 8
it was a review for the AP test were we just review everything
and I put
2cis(pi)x - 2
she marked it wrong and put a question mark over cis(pi)...

What's up with this teacher?
Do you think if I used the sis function on the AP test they would mark it wrong? It's not wrong at all...

Homework Equations

The Attempt at a Solution

 

[GreenPrint]

I mean technically
x - 2 = x + (-1)2 = x + cis(pi)2

 

[jhae2.718]

It's high school, so your teacher is probably unfamiliar with \mathrm{cis}(\theta). For the AP test, I'd recommend you stick to \frac{d}{dx}( -x^2-2x+8) = -2x-2.

I like it, though.

 

[GreenPrint]

So is there no such thing as a negative number at all sense every negative number is really just cis(pi) times a positive number? Is that why
x - 2
is really just
x + (-1)2
I always thought that was a strange property myself, simply just change the sign to positive and multiple 2 by (-1)...

 

[jhae2.718]

No, the existence of the cis function does not imply that there are no negative numbers. cis(pi) evaluates to a negative number, so you are just writing a negative number as a product of a positive number and -1.

 

[lurflurf]

At least write e^{i π}
writing cis is just silly