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mkbh_10
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Homework Statement
Locate & name the singularity of the function sin(sqrtZ)/Sqrt(Z) ?
Homework Equations
The Attempt at a Solution
At z= 0 i gives 0/0 form so should i apply L hospital's rule & then proceed ?
Correct. So, if a function has a singularity of order one what type of singularity is it?mkbh_10 said:The above function has Order =1 at z= 0 , then ?
A function with a positive order, at a given point, means that the Laurent series of the function at that point has no principle part, which means the singularity is ________.mkbh_10 said:i dn't know
A singularity in complex functions is a point at which the function is not well-defined or becomes infinite. It can occur when the function has a pole, a branch point, or a removable discontinuity.
To find the singularity of a complex function, you need to set the denominator equal to zero and solve for the values of the variable that would make the function undefined. These values are the singularities of the function.
The singularity of this complex function is at z = 0. This can be found by setting the denominator, Sqrt(Z), equal to zero and solving for Z.
The type of singularity in a complex function can be determined by analyzing the behavior of the function near the singularity point. If the function approaches infinity, it is a pole. If the function has a jump or discontinuity, it is a branch point. If the function is well-defined and continuous, it is a removable singularity.
Yes, complex functions can have multiple singularities. These can be poles, branch points, or removable singularities. It is important to identify all singularities in order to fully understand the behavior of the function.