This boggles my mind. There are so many things seemingly wrong with it, including raising a positive number to a power to arrive at a negative number. @_@; This is what I get for skimming through xkcd's archive. =(

Not sure if this will help, though, probably because you're dealing with a complex function http://img440.imageshack.us/img440/9922/zzznv3.jpg

I just used google's calculator. This also means 535.49165552476473650^i = 1 = 535.49165552476473650^0 and sqrt(535.49165552476473650)^i = -1. Another fun thing (535.49165552476473650^i)^i = 1^i But, (535.49165552476473650^i)^i = 535.49165552476473650^(i*i) = 535.49165552476473650^(-1) = 1/535.49165552476473650 = 0.00186744273 and 1^i = 1 So, e^(2π*i*i) != (e^(2π*i))^i =(

I'm confused; if you raise a number by the square root of -1, how many times are you multiplying or dividing by itself? I know a^2 = a multiplied by a and a^n is a multiplied by a an n number of times. So if the number is not real, how does it work?

Imaginary numbers. They have an "i" after them. Depending on the exponential value on that i is, i could be equal to 1, i, -1, or, -i. You divide the exponential number by four, and the remainder determines its value. Then you multiply the value of i by its coefficient to find the value of that monomial. I hope I didn't mess anything up in that explanation >_<.

I have taken Calculus. Two semesters of it. All we really covered was limits, differentiation, integration, and applications of those. I'm nearly certain we never touched on complex numbers in my Calculus classes.

Not sure if it varies with schools, but in Hunter, Intro to Complex Variables and Theories of Functions of a Complex Variable are courses offered. Prereq for the Intro is Vector Analysis

No. I'm a little 9th grader. I'm only in Honors Advanced Algebra II. I'll get to Calculus in a few years!

seemingly is the key. The complex numbers are an extension of the real numbers. An extension that doesn't break the real number calculations but adds a great deal. Now if it was just more complicated (complex) then why bother, but it turns out that complex numbers are really usefull and actually simplify many calculations. e^itheta rules! ------- Lots of math gets extended from what is taught at school. Did you know that you can have factorials of non-integral numbers? http://www.monroeccc.edu/mnaber/tests/FactorialsandGamma.pdf Madness! ... Did you know that factorial(-1/2) = sqrt(pi) Yep a factorial of a negative number and to make it worse its not even an integer. Mathemtics is nuts.:lol:

Oh. My. God. That makes NO sense (I'm sure it does of course really it's just quite overwhelming because well everything I thought a factorial WAS it isn't lol). EDIT: A simple google search makes all clear