How to determine the modulus of a complex number?

All complex numbers are in the form a+bi where a is the real part of the complex number and b is the imaginary part. Therefore if we are plotting the complex number on argand diagram the value of a tells us where the real part lies (i.e the x value) and the value of b tells us where the imaginary part is (i.e the y value).

The modulus is the distance from the origin to this point, so can be found using pythagorus' theorem. Therefore if z is the modulus z^2=a^2+b^2. We can see this method will work wherever the point is on the argand diagram and so know that sqrt(a^2+b^2) will always give us the modulus of a complex number.