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.