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# Comples Variables : Limits

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5. Show that the limit of the function

_
f (z) = ( z / z )2

as z tends to 0 does not exist. Do this by letting nonzero points z = (x, 0) and z = (x, x) approach the origin. (Note that it is not sufficient to simply consider points z = (x, 0) and z =(0, y).

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Limits are investigated for complex variables.

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5. Show that the limit of the function

_
f (z) = ( z / z )2

as z tends to 0 does not exist. Do this by letting nonzero points z = (x, 0) and z = (x, x) approach the origin. (Note that it is not sufficient to simply consider points z = (x, 0) and z =(0, y).

Solution:

When we deal with complex functions and complex variables, we have to take into account ...

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