Being z a complex number:
[tex]z=x+iy[/tex]The modulus of z is:
[tex]\lvert z\rvert=\sqrt[]{x^2+y^2}[/tex]For the given complex number:
[tex]\begin{gathered} z=6-3i \\ \\ \lvert z\rvert=\sqrt[]{6^2+(-3)^2} \\ \lvert z\rvert=\sqrt[]{36+9} \\ \lvert z\rvert=\sqrt[]{45} \\ \\ \text{Simplify:} \\ \lvert z\rvert=\sqrt[]{5\cdot3^2} \\ \lvert z\rvert=3\sqrt[]{5} \end{gathered}[/tex]Then, the modulus of the given complex number is 3√5