Why is imaginary number s important for Electrical Engineering? Without it, it's impossible to analyze the electric circuit. We tell you why. www.iklearn.com
How does this video answers the title question? I hope you understand that the final equation, which everybody uses, don't contain any imaginary analysis and are a result of simple vector analysis.
The equation for dV/dt shown starting at approximately 2:05 is simply wrong. j times sin(omega t) is _not_ the same as sin(omega t + pi/2), that equation only would be right if you used complex exponential functions instead of the sines.