Why use the z-component of the magnetic moment to find the magnitude?

[oddiseas]

Homework Statement

An electron has a magnetic quantum number m=2.What is the magnitude of the orbital magnetic moment.

Homework Equations

mu=eL/2m

The Attempt at a Solution

Now i figured that the above equation gives the magnitude of the orbital moment and the equation for the z component gives us the direction in which it points. The solution is eh/m, which means that the z component was used to find the magnitude. This has me confused, because with the angular momentum we use L,to find the magnitude and L(z) for the z component.
Why have they used the z component of the magnetic moment to find the magnitude?

 

[vela]

Either the solutions are wrong, or you misread the question and it asked for the z-component of the magnetic moment.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/orbmag.html