Convert AC Waveform from Polar to Rectangular with Phaser

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Converting an AC waveform from polar to rectangular form involves representing the waveform as v(t) = x + jy, where x and y correspond to the cosine and sine of the phase angle, respectively. The discussion highlights confusion regarding the inclusion of complex numbers in this conversion, as the original waveform appears to consist solely of real values. It clarifies that the phase angle is derived from the arctangent of the imaginary over real components. The participants question the accuracy of the representation and whether the complex component (jx) is necessary, suggesting that it might not impact the real value of v(t). Ultimately, the conversation emphasizes the importance of understanding complex numbers in AC waveform analysis.
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When converting an AC waveform (from polar) to a rectangular form, a source quotes v(t) as x + jy.

But how is this possible?...I mean v(t) is clearly the x-axis length of r (vm).

Further more how does complex number come into the picture?...every thing is real.
 
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Is my source wrong?
 
Are you not getting the question?
 
dE_logics said:
When converting an AC waveform (from polar) to a rectangular form, a source quotes v(t) as x + jy.

But how is this possible?...I mean v(t) is clearly the x-axis length of r (vm).

Further more how does complex number come into the picture?...every thing is real.

in a polar form, you'll have the magnitude and a phase where a phase is nothing but actan(imaginary/real).

thus in rectangular form indeed, you you'll have v(t) = x +jy wheer x = cos(phase) and y = sin(phase).

Ok?
 
Ok so one of the axes will return a wrong value...right?

So how come v(t) = y + jx?; I mean it should be v(t) = y...the jx doesn't make a difference?
 
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