Sunday, September 23, 2007

what is e raised to i * Pi

The other day i was seeing some presentation . During the presentation i came across a mathematical puzzle . The puzzle asked about what is the value of

value = e ^ (i * Pi) ??

now this would have been really really easy if i was in 12 th grade . But Since its a been long time since 12 th grade and few yrs since by B.S degree . It took some thinking ..

So the solution is :

well if you remember complex numbers then then you can say

e ^ (i * x ) = cos (x) + i sin(x)

so e ^ ( i * Pi ) = cos (Pi) + i sin (Pi)

since cos (pi) = -1
sin (pi ) = 0

e ^ (i * pi) = -1

Duh .. so much for my memory :( ..