1 Topic by Peter (edited by Peter 2013-09-23 09:19:25)

Topic: Complex number modulus

I have been trying to create a graph that will give the modulus of {(a+bi)^i  or  z^i } as a function of the argument of z where z is a complex number and i the imaginary unit. For positive values of b, |z^i| =e^(-arg(z)) and for negative values of b, |z^i| =e^(arg(z)). I have tried various parametric equations with no success. The closest I can get is f(x)=e^(-x) but this is only accurate in the range –pi to pi. If I could repeat this graph at every odd multiple of pi then this would do, but because I have no mathematical  knowledge, I don’t know what the heck I’m doing. Any suggestions please?

Re: Complex number modulus

I am unsure what it is exactly you are asking for, but the function f(x)=e^(-mod(x+pi,2pi)+pi) will repeat e^-x for every 2pi starting at x=pi.

Re: Complex number modulus

Thank you Ivan this is exactly what I was looking for. Sorry I couldn’t be more specific, but my lack of math doesn’t allow me to. This is my simple explanation (hopefully correct)of the function :  in the complex plane take a straight line emanating from the origin, every point (z) along this line when raised to the power of i (the imaginary unit) will result in a point that lies on the circumference of a circle centred on the origin. The radius of this circle is a function of the angle of the original line. Referring to your equation:  The graph represents the complex plane, consider any point along the x axis as representing the angle (in radians) that any complex number makes with the positive x axis (0 to pi anticlockwise, 0 to –pi clockwise), any point (z) along a line with this angle when raised to the power of i will result in a point that lies on a circle with a radius of f(x), the function you have provided. As I am not math savvy I don’t understand the function or why it works but I will make a firm effort to do both. Thank you again Ivan.