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# Multiplying by j is rotation

Successive powers of the imaginary unit j correspond to a rotation.  Created by Willy McAllister.

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• This is the most valuable explanation of "j" essence I've ever met. Thank you Willy!
• Hello!
Why do we use real part for resistors and imaginary part for capacitors and coils?
Thank you
• Resistors, capacitors, and inductors each have a specific real-world behaviors. We create mathematical models that come as close as possible to what we see happening in real life.

For a resistor by itself the mathematical model is called Ohm's Law. The capacitor and inductor have similar i-v laws.

When we make combinations of R, L, and C, AND we limit ourselves to sine wave shaped signals, the mathematical model that seems most useful describes the i-v behavior using a complex number, with R in the real part and L or C in the imaginary part.
• Thanks for this video.
at you say "there is no real part."
Should it not have been "there is no imaginary part."
(1 vote)
• Likewise, I just noticed he says "there's no REAL part", for j to the zero, when he must mean there's no IMAGINARY part. These little mistakes make it VERY confusing for the student, and shouldn't take but a moment to correct.
(1 vote)
• You are correct. I had a brain cramp while recording the video, and only found it much later. The corrected video is on my site
spinningnumbers dot org.

The video is listed in the AC Analysis section.
(1 vote)
• The 1 on the complex plane is also 0.
(1 vote)
• Luckily I had just studied this in Algebra 2 so this made this lesson much easier to understand.
(1 vote)