modulus (of a complex number)

How far a complex number sits from the origin — its distance, written |z|.

For a nonzero complex number $z=a+bi$ , the modulus is its distance from the origin, $r=|z|=\sqrt{a^2+b^2}$ — the same quantity as the number's absolute value, now read off the complex plane. Together with the argument, the modulus gives the number's polar form $z=r(\cos\theta+i\sin\theta)$ .