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Phasor notation

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



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



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