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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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.

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David Goodmanson
David Goodmanson 2022년 5월 21일
Hello Aisha,
technically this equation should read
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.

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