I don't think that's what you meant. Try again.ThLiOp said:r = |z3|
A singularity of a complex function is a point in the complex plane where the function is not defined or where it becomes infinite. It is an essential concept in complex analysis and is often associated with the behavior of a function near that point.
The three main types of singularities are removable, essential, and poles. A removable singularity is a point where the function can be extended to be continuous. An essential singularity is a point where the function has infinite oscillation. A pole is a point where the function becomes infinite.
Singularities are classified based on their behavior near the point. This includes the order of the singularity, which is determined by the highest power of the variable in the Laurent series expansion, and the type of singularity, which is determined by the convergence or divergence of the Laurent series.
Singularities play a crucial role in complex analysis as they can reveal important information about the behavior of a function. They are also used to classify and analyze the properties of complex functions, such as analyticity and differentiability.
In complex function analysis, singularities are often handled through techniques such as the Cauchy integral theorem and residue theorem. These tools allow us to evaluate complex integrals and understand the behavior of a function near a singularity.