User talk:76.18.202.211

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Your request to be unblocked has been granted for the following reason(s):

Autoblock of 76.18.202.211 lifted or expired.

Request handled by: John Reaves (talk) 03:32, 7 April 2007 (UTC)

[edit] Hello!

Hi, 76.18.202.211

I noticed your comment over on this article, that the word "abelian" should be capitalized. So I thought this discussion might be of interest.

I'm also curious about your comment on complex number, that the article is too hard to understand. Are you serious? Or is that just a joke (they are, after all, complex numbers).  ;^> DavidCBryant 11:19, 23 April 2007 (UTC)

Hello again. I got your message. Thanks for writing back.
Complex numbers aren't really any harder than other kinds of numbers. The first thing you have to learn about them is that there's a special number called the imaginary unit i. This special number has the very special property that i2 = −1. Since (−1)2 = 1, we must also have (−i)2 = (−1)2i2 = i2 = −1.
All the rest of the properties of complex numbers are fairly easy to work out once you wrap your head around these basic facts about the imaginary unit i. Go ahead and ask me questions about the article if you like, and I'll try to explain anything that seems unclear. DavidCBryant 00:03, 24 April 2007 (UTC)

[edit] Arctan

Hello again.

Thanks for the very kind words on my talk page. I know the formula for finding the argument of a complex number looks pretty intimidating. But it's not really that hard to understand. The inverse tangent function (arctan) has its "principal branch" from −½π to ½π (OK, from −90° to 90°, if you prefer to measure angles in degrees). The reason for that is pretty simple – tanθ = sinθ/cosθ, and since cos(−½π) = cos(½π) (both are zero), that's where the tangent function "blows up", approaching infinity at those two angles. So arctan can't be smoothly defined at those two angles.

I never think of that silly arctangent formula, anyway. I just think about the four quadrants of the plane. In quadrant 1, both x and y are positive. In quadrant 2, x is negative and y is positive. In quadrant 3 both x and y are negative, and in quadrant 4 x is positive and y is negative. So then the "argument" of a complex number just runs from −π to −½π in quadrant 3, from −½π to zero in quadrant 4, from zero to ½π in quadrant 1, and from ½π to π in quadrant 2. That's how I remember it, anyway.

Good luck with Algebra II! DavidCBryant 21:52, 3 May 2007 (UTC)