Question

For some reason I am not getting the right answer on what I thought was an easy problem:

Answer 1

Given
\[\Large z=e^{2\pi i/5}\] Evaluate \[ \Large 1+z+z^2+z^3+5z^4+4z^5+4z^6+4z^7+4z^8+5z^9\]

Answer 2

Try this: http://doiop.com/euler

Answer 3

lol

Answer 4

get real

Answer 5

how are u determining whre to put 5 and the 4s

Answer 6

OHHHH Wow it was a trick question nevermind. I had the right answer I just wasn't looking carefully enough at the answer choices.

Answer 7

okk

Answer 8

I put \[\Large 5 e^{4\pi i/5}\] but the right answer was \[\Large -5e^{3 \pi i/5}\] very tricky. The question is very easy to solve though lol.

Answer 9

See what you do is you know that \[\Large 1+z+z^2+z^3+z^4 =0\] since they are all like equally spaced vectors in equilibrium so you can do this and it leaves just he last term lol.

Answer 10

oh now i see why the 5 and 4s

Answer 11

so why does this equal spacing give u 0 all the time

Answer 12

It's just like how (-1)^0 + (-1)^1=0 or \[\Large i^0+i^1+i^2+i^3=0\]

Answer 13

similiar to that question u posted earlier

Answer 14

how to find that center of n polygon

Answer 15

all the vectors formed by e^(2pi/n)
when added up will result in an n polygon

Answer 16

Yeah haha exactly.

Answer 17

but somehow adding up these same vectors infinitely gives you their average here lul. Or t least 1/(1-z) does if you don't want to think of an infinite series as an averaging over infinity