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

Jan 15, 2018

Complete the square

#### Explanation:

so it can be written as
${a}^{2} + \frac{1}{{a}^{2}} - 2 \cdot a \cdot \frac{1}{a} + 4 i \left(a + \frac{1}{a}\right)$ = ${\left(a + \frac{1}{a}\right)}^{2} + 4 i \left(a + \frac{1}{a}\right)$
which is the same as
$\left(a + \frac{1}{a}\right) \left(a + \frac{1}{a} + 4 i\right)$
now take $\left(a + \frac{1}{a}\right) = t$
hence roots are
$t \left(t + 4 i\right)$

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

hope u find it helpful :)