# Is it possible to find the limit as a function approaches a complex number?

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Paul Rubino on 12 Nov 2022
Edited: Bruno Luong on 13 Nov 2022
Hello
I am trying to find the limit of a function as it approaches a complex number but I get an error that says "Limit Points must be real, 'infinity', or '-infinity'". Does anyone know if there are work arounds for complex limits in matlab or if this is just not a supported functinality of the software?
syms m2
limit(m2,m2,complex(1,1))
Here is some small sample code that produces the same error I am encountering.
Here is some context for the problem I am working on for those who might be interested.

Walter Roberson on 12 Nov 2022
The MATLAB limit function calculates the limit from below and the limit from above, and tells you the limit is undefined if the two are not equal.
If you were working with complex numbers then there are not just two directions to consider, there are an infinite number of directions to consider. Complex numbers can be characterized by magnitude and angle, and in a limit you would shrink the magnitude towards 0 but that leaves open all angles. The limit along angle π/5 might be different than the limit along 3π/11 or π+1/18. So taking a complex limit turns into a proof that the limit does not vary with complex angle, rather than simply evaluating the limit at two specific angles and comparing them.
Bruno Luong on 13 Nov 2022
Edited: Bruno Luong on 13 Nov 2022
Read diagonally the debate it looks like there is a confusion by Walter of
• the limit directional about a single point (even it's the same does NOT ensure the limits to a value) and
• argument (angle) of two points related to the origin of complex plane.
Those are entirely different.

Bruno Luong on 13 Nov 2022
Edited: Bruno Luong on 13 Nov 2022
If seem that what you want can be derived from the the Laurent series of G about p_i
I have no idea if Matlab symbolc can compute Laurent series (I don't have the toolbox, but I see it mentions in taylor document page)

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