Question

hot to proceed further​

Answer 1

Answer:

I think ,

$\frac{1}{(x - i)(x +i )} = \frac{a}{(x - i)} + \frac{b}{(x + i)} \\ \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = a(x - i) + b (x + i) \\ \\ put \: x = \: i \\ we \: get \: \: .\: 1 = b(2i) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: b= \frac{1}{2} i \\ put \: x = \: - i \\ we \: get \: \: \: 1 = a( - 2i) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = - \frac{1}{2} i$

therefore,

A= -1/2 i

B= 1/2 i