Chọn D
\(4z^{2} -4z+3=0\Leftrightarrow \left(2z-1\right)^{2} =-2\Leftrightarrow \left(2z-1\right)^{2} =2i^{2} \)
\( \Leftrightarrow \left[\begin{array}{l} {2z_{1}^{} -1=i\sqrt{2} } \\ {2z_{2}^{} -1=-i\sqrt{2} } \end{array}\right. \Leftrightarrow \left[\begin{array}{l} {z_{1}^{} =\frac{1}{2} +\frac{\sqrt{2} }{2} i} \\ {z_{2}^{} =\frac{1}{2} -\frac{\sqrt{2} }{2} i} \end{array}\right. . \)
\(\left|z_{1}^{} \right|+\left|z_{2}^{} \right|=2\sqrt{\left(\frac{1}{2} \right)^{2} +\left(\frac{\sqrt{2} }{2} \right)^{2} } =\sqrt{3} . \)