Problem in transition from phasor to normal

[nhrock3]

oiler formula says
cosx+isinx

but here they multiply by minus the imaginary part of the phasor representation
the coefficient of sine is minus the imaginary part
why??

 

[LCKurtz]

oiler formula says
cosx+isinx

That's "Euler" formula. A Frenchman, not a oil tanker. And I suppose you mean the identity

$$e^{ix} = \cos x + i\sin x$$

but here they multiply by minus the imaginary part of the phasor representation
the coefficient of sine is minus the imaginary part
why??

I have no idea what your image has to do with your question. Do you mean this? :

$$e^{-ix} = \cos{(- x)} + i\sin {(-x)} = \cos x - i\sin x$$

 

[CEL]

That's "Euler" formula. A Frenchman, not a oil tanker. And I suppose you mean the identity

A nitpick: Euler was Swiss, not French.

 

[LCKurtz]

A nitpick: Euler was Swiss, not French.

You are right! And I see upon looking him up, I would also have misspelled his first name had I mentioned it.

 

[DeeNos]

The reason for the coefficient of sine being the negative imaginary part in this case is due to the way complex numbers are represented in the phasor domain. In the phasor domain, a complex number is represented as a magnitude and phase angle, while in the normal domain, it is represented as a real and imaginary part.

When converting from the phasor domain to the normal domain, the magnitude remains the same, but the phase angle is converted to the imaginary part. Since the phase angle in this case is -90 degrees, the imaginary part in the normal domain will be -1. This is why when using the oiler formula, the coefficient of sine is the negative imaginary part.

It is important to remember that these representations are just different ways of expressing the same complex number and do not change the underlying mathematical principles. It is a common practice to use the negative imaginary part in the normal domain when converting from the phasor domain, but it is also possible to use the positive imaginary part by adjusting the phase angle accordingly. Ultimately, it is a matter of preference and ensuring consistency in calculations.