Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2011-06-09 04:47:27

MathPro101
Member
Registered: 2011-06-08
Posts: 18

Complex Equation

I found this video on youtube of an MIT Physics lecture. If you jump ahead to around 45 minutes, the professor offers a math problem that I found interesting.

http://www.youtube.com/watch?v=OvDePn41fPY

It took me a long time to work through it, but if you know the trick, it can be solved in less than 10 seconds.


i^i, where i = sqrt(-1)

the clue is that i=e^i(pi/2 plusminus 2*pi*n), n=0,1,2,...


Have fun with it, let me know what you think.

Offline

#2 2011-06-18 02:40:07

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Complex Equation

. .

. .


. .

. .

.

Offline

#3 2011-06-18 05:54:56

MathPro101
Member
Registered: 2011-06-08
Posts: 18

Re: Complex Equation

Very Good! One quick addition to that would be to say that θ = π/2 ± 2πn, where n=0,1,2,.. This is the same as rotating on the unit circle and getting back to the same place each time. Therefore the true answer should be e^(-π/2 ± 2πn), which is still a real number!

There is another way of solving this problem that uses a different technique. Can anyone figure that one out? It simplifies things greatly.

Offline

Board footer

Powered by FluxBB