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Illustration Impedance phasor - magnitude and phase angle in the complex plane

<span>Impedance phasor - magnitude and phase angle in the complex plane</span>
Impedance phasor - magnitude and phase angle in the complex plane
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Impedance (complex resistance) represented as a phasor \( \boldsymbol{Z} \) in a complex plane. The complex plane together with the phasor forms a phasor diagram. The horizontal axis forms the real part of \( \boldsymbol{Z} \) and the vertical axis forms the imaginary part of \( \boldsymbol{Z} \).

The phasor rotates counterclockwise. Here it is shown at a certain point in time. The phasor has a magnitude \( |\boldsymbol{Z}| \) which represents the length of the phasor. Also, the phasor includes a phase angle \( \varphi \) with the real axis.

The magnitude and phase angle uniquely define the phasor:$$ \boldsymbol{Z} ~=~ |\boldsymbol{Z}| \, \text{e}^{\text{i}\,\varphi} $$