Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

What am I doing wrong?

But my book says

Thanks.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: What am I doing wrong?

You're not wrong, you just need one more step to get the answers to match.
Use the same trick that you did to get from line 4 to 5.

---

Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: What am I doing wrong?

Ahh okay, thanks

Nils-Ake

Member

Registered: 2008-04-15

Posts: 20

Re: What am I doing wrong?

Hi Daniel. I don't get this:

Could you explain it please? :)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: What am I doing wrong?

The sum of the nth roots of unity will always give 0. Proof:

This can also be 'seen' if you think of each of the roots as vectors. The argument of each root increases by 2pi/n each time, so adding n of them will give a regular polygon with n sides, returning to the starting point (ie a vector sum of zero).

Actually, this isn't just true for nth roots of unity; it's true for nth roots of all complex numbers.

Last edited by Daniel123 (2008-11-24 11:19:42)

Nils-Ake

Member

Registered: 2008-04-15

Posts: 20

Re: What am I doing wrong?

Ahh I didn't know that

were the nth roots of unity. Now it makes perfect sense. Thanks!

(typo)

Last edited by Nils-Ake (2008-11-25 00:38:21)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: What am I doing wrong?