One way to do this is with the general formula #|a+bi|=\sqrt{a^2+b^2}# so that #|3-4i|=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5#. This formula is essentially the distance formula from the point #(a,b)# to the origin #(0,0)# in the plane (in rectangular coordinates), which comes from the Pythagorean Theorem.

Another way to show your work if #z=a+bi# is to write the answer as #|z|=sqrt(z*\bar{z})#, where #\bar{z}=a-bi# is the complex conjugate of #z#. Since #z*\bar{z}=(a+bi)(a-bi)=a^2-abi+abi-b^2i^2=a^2+b^2#, this gives the same answer.