Advanced Math

Question : how to find singularities of cot z. Solution : Singularities of cot z Since we can write \[cot\ z\ =\frac{\cos{z}}{\sin{z}}=\frac{p\left(z\right)}{q\left(z\right)}\] Singularities of cot z are the zeros of…

Question : Prove that each singular point of tan z is a simple pole. Solution : Singularities of tan z Since we can write \[tan\ z\ =\frac{\sin{z}}{\cos{z}}=\frac{p\left(z\right)}{q\left(z\right)}\] Singularities of tan…

Question : how to Find zeros of tan z and cot z Solution : (a)zeros of tan z We can write \[tan\ z\ =\frac{\sin{z}}{\cos{z}}\] Now zeros of tan z are…

Question : Show that sin(z)/z has removable singularity at 0 Solution : Given function \[f(z)\ =\frac{sin\left(z\right)}{z}\] To that sin(z)/z has removable singularity at 0 First we shall find it’s Laurent…

Question : What is an isolated singularity? Explain with examples Solution : Isolated Singularity : A singular point z0 is called an isolated singularity of a function f(z) if f(z)…