# Complex numbers/Polar coordinates/Angle naive/Example

Every complex number , , can be written uniquely as

with a positive real number , which is the distance between and the zero point
(thus,
)
and an angle between and below degree, measured counterclockwise starting with the positive real axis. The pair constitutes the *polar coordinates* of the complex number.

Polar coordinates in the real plane and for complex numbers are the same. However, the polar coordinates allow a new interpretation of the multiplication of complex numbers: Because of

(where we have used the addition theorems for sine and cosine), one can multiply two complex numbers by multiplying their modulus and adding their angles.