130 reputation
6
bio website calebmadrigal.com
location Milwaukee, WI
age 28
visits member for 2 years, 7 months
seen Mar 5 at 22:53

I am both a professional and enthusiast programmer. I currently work as a software consultant at SpiderLogic. My most recent project work has been done in: Java, Objective-C, Python, C. I'm also doing some Scheme programming and Arduino development on the side.


Jul
11
awarded  Popular Question
Aug
23
asked Waves of differing frequency are orthogonal - help me understand
Jan
31
awarded  Supporter
Jan
31
accepted How does $e^{i x}$ produce rotation around the imaginary unit circle?
Jan
31
comment How does $e^{i x}$ produce rotation around the imaginary unit circle?
Ok, I think this helps me understand it. As you raise i to integer powers, it ends up rotating around the imaginary unit circle: $i^0=1$, $i^1=i$, $i^2=-1$, $i^3=-i$, and $i^4=1$. These positions (1, i, -1, -1) correspond the the following (x,y) positions: (1,0), (0,1), (-1,0), (0,-1). So it makes sense that multiplying the current position by i would result in a 90 degree ($\pi/2$) rotation.
Jan
31
awarded  Student
Jan
31
awarded  Editor
Jan
31
comment How does $e^{i x}$ produce rotation around the imaginary unit circle?
Oops. Yep. Fixed.
Jan
31
revised How does $e^{i x}$ produce rotation around the imaginary unit circle?
deleted 7 characters in body
Jan
31
comment How does $e^{i x}$ produce rotation around the imaginary unit circle?
@manu-fatto The exponential function is simply e (2.718...) raised to a power.
Jan
31
revised How does $e^{i x}$ produce rotation around the imaginary unit circle?
edited tags
Jan
31
asked How does $e^{i x}$ produce rotation around the imaginary unit circle?
Feb
13
awarded  Scholar
Feb
13
accepted Solving barometric formulae for height
Feb
12
comment Solving barometric formulae for height
@BenCrowell: Yes, I know I need the 2 equations. One for lower altitudes, and the other for higher.
Feb
12
asked Solving barometric formulae for height
Feb
12
awarded  Autobiographer