Fp3 Help

https://2d31ca6ec4f6115572728c3a9168ad5dfc897f33.googledrive.com/host/0B1ZiqBksUHNYSjAyWFYyQmU5Tjg/OCR/FP3%20Complex%20Numbers.pdf


q1ii?

How am I supposed to draw it?
Like I don't know what 1+w is, if someone can explain how to work that out.

$w=\cos\left(\frac{2\pi}{5}\right)+i\sin\left(\frac{2\pi}{5}\right)$
So $1+w=1+\cos(\frac{2\pi}{5})+i\sin(\frac{2\pi}{5})$
Use De Moivres Theorem such that
$w^{n}=\cos(\frac{2n\pi}{5})+I(\frac{2n\pi}{5})$
Forget the n preceding the isin
Then you just draw a nice spiral.

What happens to the one after the De Moivre's bit?

$w=\cos\left(\frac{2\pi}{5}\right)+i\sin\left(\frac{2\pi}{5}\right)$
So $1+w=1+\cos(\frac{2\pi}{5})+i\sin(\frac{2\pi}{5})$
Use De Moivres Theorem such that
$w^{n}=\cos(\frac{2n\pi}{5})+i \sin ( \frac{2n\pi}{5})$

What happens to the one after the De Moivre's bit?

Yeah, dunno what the other user is doing... just think of them as vectors. So you move 1 unit along the real plane to the right and then tack on the vector w and move in that direction, for w^2 you just move from your previous position along the direction of w^2. You should dint that you end up at the origin again once you've drawn the one with w^4. (think back to roots of unity and how they form vertices of special geometric shapes)

How do you know that 1+w causes the point to move to the right of 1 and that 1+w+w^2 causes it to move to the left of 1+w? I'm looking at the ms atm. I don't quite get how you work out the direction

Angle of 2pi/5, that's obviously to the right. Angle of 4pi/5 is obviously to the left, etc...

Then you just draw a nice spiral.