Find the square root of the following complex number :

$\displaystyle 6+8i $

$\displaystyle \sqrt{6+8i}=a+bi$

$\displaystyle 6+8i=a^2-b^2+2abi$

$\displaystyle

a^2-b^2=6 ----1

$

$\displaystyle 2ab=8 ---- 2$

From 2 , $\displaystyle b=\frac{4}{a}$

Substitute into 1 : $\displaystyle a^2-\frac{16}{a^2}=6$ which gives me

$\displaystyle a=\pm2\sqrt{2}$

then $\displaystyle b=\pm\frac{2}{\sqrt{2}}$

did i get the correct answers for a and b ? THanks for helping .