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The equation for adding sinusoidal functions which differ in phase resembles the equation for adding the x (or y or imaginary) components of vectors which are rotating in the xy or complex number plane. It is often more convenient to work with these (non-existent) vectors than with the functions. This especially true with vectors represented by imaginary ...

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The "real" part of wave function is no more real than the imaginary part. Both these parts are equally real or equally imaginary. None of them can independently describe the physical reality. Only when both these part are taken together then they represent the physical reality. Either one of them can be termed real or imaginary. Since complex numbers ...

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Well, first of all, a complex series RLC circuit can be analyzed using the following method. The total impedance of the circuit is given by: $$\underline{\text{Z}}_{\space\text{in}}=\text{R}+\text{j}\omega\text{L}+\frac{1}{\text{j}\omega\text{C}}\tag1$$ The input voltage can be written as: \underline{\text{V}}_{\space\text{in}}=\hat{\text{u}}\exp\left(\...

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