Can someone show me how to find the limit of a complex function?
Example:
z1 = 3 + 4*I
some_function[z] = z * z1
Set-up:
Limit[some_function[z],z->z1]
The result should be
(4*I + 3)*z
but I get
Limit[some_function[z], z -> 3 + 4 I]
What am I doing wrong? I tried to search in google and in the help files in the section about complex analysis.
Thank you for your attention.
can't use _ in names. the _ is used for patterns. Also your function definitions are not correct. Need to use delay assignment :=
May be this will work for you:
ClearAll[z, z1];
z1 = 3 + 4*I;
someFunction[z_] := z*z1;
Limit[someFunction[z], z -> z1]
(*-7 + 24 I*)
see DefiningFunctions.html and what-are-the-most-common-pitfalls-awaiting-new-users
Taking a sample complex function as example with z->1+i
eq = z^2 - 2 z + 1;
Separating complex and Real part,
eqt = ComplexExpand[eq //. {z -> x + I y}]
1 - 2 x + x^2 - y^2 + I (-2 y + 2 x y)
Taking real part,
Cases[eqt, x_ /; FreeQ[x, I]] /. List -> Plus
1 - 2 x + x^2 - y^2 Calculating limit for real part as,
Limit[Limit[1 - 2 x + x^2 - y^2, x -> 1], y -> 1]
-1
Taking Complex part,
Complement[eqt, 1 - 2 x + x^2 - y^2]
I (-2 y + 2 x y) Taking limit as,
Limit[Limit[(-2 y + 2 x y), x -> 1], y -> 1]
0
So, by theorems of Complex Analysis its limit is -1.
Use Example 2.17 on this Page
