Bode Plots - Absolute Value of Complex Function in Magnitude calculation
You should do some revision on complex numbers, e.g. the magnitude of a complex number, \$(a+jb)\$, is \$\sqrt{ (a^2+b^2)}\$ and not \$\sqrt{(a+jb)^2}\$, which is meaningless in this context - you should recognise that \$\sqrt {(a+jb)^2} = a+jb\$. Similarly, the phase angle of  \$(a+jb)\$ is \$arctan (\frac{b}{a})\$.

Magnitude and phase angle are scalar quantities, therefore there can't be any 'j' terms in these expressions.