Euler's indentity [ e^(πi) = -1] (2 Viewers)

[kurt.physics]

Hey, hows it going,

I was talking to the ext. 2 maths teacher today, he said you guys (im not in ext2) learn how to prove e^(πi) = -1, but when he wrote it up on the board, he wrote e^(π * -i) = -1, is this true.

Does anyone have a copy of the proof?

Thanks,

≈≈Kurt≈≈

 

[undalay]

I think Euler's out of the current 4u course.

e^(xi) = cos x + i sin x (euler's formula)
Subbing in pi
cos (pi) + i sin (pi) = -1

 

[Slidey]

e^(i*pi)=-1 because e^(2k*pi*i)=-1, k an integer
Why? Same reason cis(2k*pi+@)=a
Or why sin(pi)=sin(2k*pi+pi)=0

Interestingly, ln(-1)=2k*pi*i.

You can also use euler's formula to express sin and cos in terms of exponentials. Same for hyperbolic trig.

 

[YannY]

wtf bro
e^(2k*pi*i)=1 not -1 if k is an integer.
it only = -l if k is an odd number divded by 2. in other words only if 2k=odd number jeez..

Yeah and euler was a weird one, some would say he wasted his life studying others say he liked studying and since its fun to him then its not wasting. but i say its bother - btw he had a degree in astronomy, physics, medicine and mathematics. maybe more i cant think of anything else

 

[kurt.physics]

Do you get to learn how to prove eulers formula

e^(iø) = cos ø + i sin ø

where ø = theta

because i can comprehend everything after that its just would like to understand why e^(iø) = cos ø + i sin ø