help with complex roots of unity (1 Viewer)

[jazzyphaye]

z to the power of 5 = 0

so z to the power of 4 is the conjugate of z to the power of 3..

i don't get why z3 + z3conjugate = 2cos(4pi/5)

cause how does cos(-4pi/5) + cos(4pi/5) = 2cos(4pi/5)

 

[Trebla]

z to the power of 5 = 0

so z to the power of 4 is the conjugate of z to the power of 3..

i don't get why z3 + z3conjugate = 2cos(4pi/5)

cause how does cos(-4pi/5) + cos(4pi/5) = 2cos(4pi/5)

Recall that cos (-x) = cos x (i.e. cos x is an even function)
and sin (-x) = - sin x (i.e. sin x is an odd function)
When you sum cis (4π/5) and cis (-4π/5) which is its conjugate you end up with:
cos (4π/5) + isin (4π/5) + cos (-4π/5) + isin (-4π/5)
= cos (4π/5) + isin (4π/5) + cos (4π/5) - isin (4π/5)
= 2cos (4π/5)

 

[jazzyphaye]

but i still donn't get it.. like

say x=144

cos144 doesn't equal cos(-144)

 

[Trebla]

but i still donn't get it.. like

say x=144

cos144 doesn't equal cos(-144)

They are equal: cos 144 = cos (-144), even check on your calculator.

 

[Zeber]

Draw the ASTC graph, you'll note that cos(x) = cos(-x) for whatver values of x.

 

[Pwnage101]

its an EVEN function - now if u aint gettin what it means by even, dunno y ur doin 4u...

 

[jazzyphaye]

oh shit sorry i get it. brain lag.

thanks!

and to:
pwnage101 .. STFU don't question why i'm doing 4u SORRY i came across a lag and SORRY we're not all little miss smart and perfect.