# How to plot the magnitude and the phase of this function f(1/z)=(0.5 + 000i)*z^(−1 )+ (0.2500 − 0.4330i)*z^(−2) + (−0.2500 − 0.4330i)*z^(−3)?

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Aisha Mohamed on 18 May 2022
Answered: David Goodmanson on 21 May 2022
Thank you for every one helped me to understand how to plot comples function ,Torsten and David xplain ed different ways to plot this function which finally gave the same result.(Many thanks)
In my question, when this function is in(1/z) .
How can we plot this function
f(1/z)=(0.5 + 000i)*z^(−1 )+ (0.2500 − 0.4330i)*z^(−2) + (−0.2500 − 0.4330i)*z^(−3)?
I appreciate any help.

David Goodmanson on 21 May 2022
Hello Aisha,
f(z)=(0.5 + 000i)*z.^(1 )+ (0.2500 0.4330i)*z.^(2) + (0.2500 0.4330i)*z.^(3)
i.e. f(z) on the left hand side. Also, using .^ instead of ^ is necessary to make progress.
From the previous answer that I posted, you can plot this in the same way. The only difference is that, since z.^(-1) goes infinite for z = 0, you have to pick a grid that does not include the point (0,0) such as
xx = -6.005:.01:60.05;
yy = -6.005:.01:6.005;
[x y] =meshgrid(xx,yy);
z = x+i*y;
Of course the closer you get to the origin with a mesh point, the larger the result is. But if you plot log(abs(z)) rather than abs(z) this is not really a problem.