Imaginary i exists

	Duration: 04:30 minutes Upload Time: 2007-12-03 00:21:46
The imaginary number i exists and the square root is -1
Comments
camgere  2008-03-17 11:38:42 Congratulations! You stumped the professor!. Honestly, I don't understand the proof, either. Wikipedia has a good explanation of "Euler's Formula". Apparently you can take a Taylor Series expansion of all three terms and prove an identity. It has to be "e". The result is very useful. __________________________________________________
blower05  2008-03-17 06:46:23 I still don't have the insight how e can be introduced into the complex number. Does it matter it does need "e" or some other symbols or variables to denote the cos(wt) + isin(wt)? __________________________________________________
staahl  2008-01-25 10:18:42 Thank you. Very informative. You might consider using a smaller font though.. __________________________________________________
camgere  2008-01-11 19:21:40 Expressing a complex number in polar co-ordinates let's your rethink the meaning of square root. The magnitude of the square root of A is the square root of the magnitude of A. This exactly conforms to our experience with the real number line. The angle of the square root of A is half the angle of A. This makes us rethink what it means to be a square root. Since I neglected mathematical rigor I'm quite happy that anybody got anything out of this. __________________________________________________
MIFFLINITY  2008-01-10 18:37:25 nice vid. the moving sinewave was cool, but i fell of at 2:44. i mean, i understand the calculations at the right side in an algebraic way, but it still doesnt make sense way the square root of minus one is equal to the square root of eulers number in the power of pi times i - in a graphical way. so, well, i guess youre right, but the thing is that you kind of start of good with explaining with the plane and axis, but yeah... well. nice to see thoser numbers anyway :) __________________________________________________