Question

1/(3+i)²+1/(3-i)² find the conjugate​

Answer 1

Step-by-step explanation:

We have,

$z = \frac{1}{(3 + i)^{2} } + \frac{1}{(3 - i)^{2} }$

$\implies \: z = \frac{1}{8 + 2i} + \frac{1}{8 - 2i}$

$\implies \: z = \frac{8 - 2i + 8 + 2i}{(8 + 2i)(8 - 2i)}$

$\implies \: z = \frac{16}{4(4 + i)(4 - i)}$

$\implies \: z = \frac{4}{16 + 1}$

$\implies \: z = \frac{4}{17}$

So, it is a purely real

Hence, its conjugate is 4/17