### Phasor notation

In **phasor notation**, you can write a complex number *z* = *a* + *bi* as

##### Explanation

In the Argand diagram, the dotted line indicates the modulus |*z*| van *z*. It is a positive real number.

The Greek letter *θ* (theta) is a real number that indicates the angle to the real *x*-axis. Since *x* = |*z*| cos *θ* and *y* = |*z*| sin *θ*, the tangent holds

From this you can take the inverse tangent which is then written as

This is called the complex argument. It is also called the *phase* or *amplitude*. The complex argument of *z* in the interval [0, 2π) is called the principal value. The interval (–π, π] is also chosen as the principal value. A complex number *z* can be written with arg (*z*) and modulus |*z*| as

##### Example 1

You can write the complex number *z* = 1 + *i* in phasor notation, because

so