An alternative and important representation of a complex number involves

the use of polar coordinates. If a complex number z is regarded as a point P

in the complex plane, it can be identified uniquely by specifying the radial

distance r from the origin to P, together with the polar angle u measured

anticlockwise from the positive real axis to the line OP. The distance r is simply the modulus of z , while the angle u is called the argument of z , and it

is written arg z . The specification of r and u is called the modulus/argument form of a complex number. The modulus/argument representation of z is shown in Fig. 43.