Question

quick euler's formula question

Answer 1

\[e^{-i n (\pi/2)}= (-i)^{n}\]

Answer 2

how to show that these two are equal?

Answer 3

You can go at this using one of the most spectacular of all maths ID's:

\(e^{i \pi} + 1 = 0\)

Not only worth remembering but actually hard to forget once you've seen it.

So split the sides out, invert it to get the negaive exponent, and then take the n/2 th root to get the finished product


You can also go one step further up the food chain. Start with Euler's formula:

\(e^{ix} = \cos x + i \sin x\)

Sub in \(x = \frac{\pi}{2}\) and go from there .... same kinda steps.