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Question

How to find removable singularity?


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Solution

Step 1: Explaining how to find removable singularity:

A removable singularity of a function is a point z0 where the function fz0 appears to be undefined. We can remove this singularity by redefining the function, then we can say we remove the singularity.

Step 2: Writing example:

f(z)=z2-1z-1 at z=1the function is undefined.

f(z) has a removable singularity.

f(z)=(z-1)(z+1)(z-1)[(a2-b2)=(a+b)(a-b)]f(z)=(z+1)

Now the function has no singularity as we removed it.

Hence, in this way, we can find removable singularity.


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