Question

Find the square roots of a^2+1/a^2+4i(a+1/a)-2?

Answer 1

Complete the square

Explanation:

so it can be written as
`a^2 + 1/(a^2) -2*a*1/a + 4i(a+1/a)` = `(a + 1/a)^2 + 4i(a + 1/a)`
which is the same as
`(a + 1/a)(a + 1/a + 4i)`
now take `(a + 1/a) = t`
hence roots are
`t(t+4i)`

hence `t` and `t+4i` are the solutions

hope u find it helpful :)