seminar assessment - HELP (1 Viewer)

[AR]

we have a seminar assessment where we have to teach something for 20 minutes in an interesting way... i dont know if everyone has it, but i can't think of anything and i need ideas!
does anyone know how to prove euler's thing: e^-i(pi) = 1?
i think that;s it... please help me!

 

[gman03]

i think you need to differentiate e^i@ w.r.t. @ and show that e^i@ is equal to cos@ + isin@, and i thought Euler's formula is not in 4U syllabus... interesting teacher you have

 

[McLake]

The way I have been shown:

Trig/exponentional expressions can be written as infinitely long polynomials:

sinx = x - x^3/3! + x^5/5! - x^/7! + .....
cosx = 1 - x^2/2! + x^4/4! - x^6/6! + ....
e^x = 1 + x/1! + x^2/2! + x^3/3! + .....


also coshx = (e^x + e^-x)/2
and sinhx = (e^x - e^-x)/2

now Re(e^ix) = cosx
so e^ix + e^-ix = 2cosx
so cosx = (e^ix + e^-ix)/2
and e^ix - e^-ix = 2isinx
so sinx = (e^ix - e^-ix)/2


so e^ix = cosx + isinx
sub x = -pi
e^-i(pi) = 1

 

[ngai]

i think you need to differentiate e^i@ w.r.t. @ and show that e^i@ is equal to cos@ + isin@, and i thought Euler's formula is not in 4U syllabus... interesting teacher you have

diff f(@) = cos@ + isin@ wrt@, then u get f'(@) = i f(@), so integrate both sides of f'(@)/f(@) = i to get lnf(@) = i@ + C
sub in @=0 to get C = 0
f(@) = cis@ = e^i@
then @ = pi

yeah euler's formula isn't in syllabus, dunno y not tho

 

[AR]

thanks

thankyou all!
so no one else has to do a seminar assessment? that makes me jealous...

 

[sammeh]

wish i could have ;o
sounds like fun.

 

[mojako]

thankyou all!
so no one else has to do a seminar assessment? that makes me jealous...

hmm can I know what school you go to?
coz its interesting to have that kind of assessment..

and.. is it allowed to assess ppl on something out of the syllabus?