# Trying to plot complex function for varying value of t

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Keaton Looper on 17 Mar 2024
Commented: Walter Roberson on 20 Mar 2024

My function is given by exp(i*t) and I want to plot the function for varying values of t. The function should show that it curves closer and closer to the imaginary axis as t increase from 0 to pi how would I show this and graph each increment on a graph? I have put an image using Desmos to show what I want matlab to graph.

Keaton Looper on 17 Mar 2024
Yes I want to show how for each value of t from 0 to pi the function curve gets closer to the imaginary axis as seen in the image above
dpb on 17 Mar 2024
You're going to have to show us how you did what you did in Desmos; it doesn't look like what you describe to me.
clear all
t=linspace(0,pi); % vary t from 0 to pi
plot(exp(i*t)) % plot the function against t
ylim(xlim) % put on even range
axis square % and the same footing in space

Binaya on 20 Mar 2024
Hi Keaton
By Euler's formula, use of the expression "exp(i*t)" results in the expression "cos(t)+i*sin(t)". From this expression, it can be concluded that the maximum value of the expression can be 1 in either real axis or imaginary axis.
When you try to plot this "exp(i*t)", where t ranges from 0 to pi, you get a half circle as shown below:
t=0:0.01:pi;
y=exp(i*t);
plot(y);axis equal;
The plot generated by desmos does not seem to take into account the "i" or imaginary number when calculating the plot of the exponential which leads to the a plot of exponential function with real inputs.
Walter Roberson on 20 Mar 2024
As a special case, if you plot() a single variable and the variable is complex-valued, then it plots imaginary component of the value versus real component of the value.