[Math] Graphing parametric complex equations

graphing-functions

I am given a group of functions that represent a decaying circle and I am trying to graph them so to better visualize them.
One of the equations I have is

z(t) = 2 * e^(-a*t) * e^(j*2*pi*0.5*t + (pi / 2)) 
for t from 0 to 4 and a = ln(3)

From this I know the following

Amplitude = 2
Decay = 1/3
Phase Shift = pi / 2 (90 degrees)
Frequency = 0.5
Period = 2

When I graph it I use parametric mode on my calculator (TI-84) and enter the following

X1T = 2e^(ln(3)*T) * (cos(2*pi*0.5*T) + cos(pi/2))
Y1T = 2e^(ln(3)*T) * (sin(2*pi*0.5*T) + sin(pi/2))

However I do not believe this is correct as the graph does not look like a normal circle that is decaying. Is this the correct graph and I am just misguided on what it should look like or did I misunderstand how to graph it?

WolframAlpha plot of it as http://bit.ly/1g2Lql9

Best Answer

I hope the following plot helps you. I made it by Maple environment using below codes:

[> with(plots):
   a := ln(3);
   complexplot(2*exp(-a*t)*exp((1/2)*(2*I)*Pi*t+(1/2)*Pi), t = 0 .. 4);

enter image description here

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