00:01
Hi, now we are going to find the poles and residues.
00:09
For finding the pole, we have to equate the denominator to 0.
00:15
So we get z squared plus 9 equal to 0, then z squared will be equal to minus 9, then z will be 3i.
00:26
Here the order of the pole is 1 and we know that residue of f of z at a point z is that equal to a is limit of z tends to a, z minus a into f of z.
00:46
From this we get residue of f of z at a point z equal to 3i will be equal to limit z tends to 3i z minus 3i into z plus 1 divided by z squared plus 9 and it will be equal to 3i plus 1 divide by 6i.
01:15
It can be written as 3 plus or minus i divide by 6.
01:20
So the residue of this sum is 3 plus or minus i divide by 6.
01:31
And next spot b, z squared plus 2 divide by z minus 1.
01:43
Then z minus 1 equal to 0, then z will be 1.
01:48
Here the order of the pole is 1...