bit of an odd question...would love a hand please?

Question

jack1 · Answer

how do i convert a 3 V 50 Hz   AC source into a phazor   

ie into real and imaginary portions
usually in the form of     2.1 + 2.7i where i = sqrt -1

unklerhaukus · Answer

something like this?
$$V=V_0\cos(kx-\omega t)$$
$$V=3[\text V]\cos\big(kx-50[\text{Hz}]\times t[\text s]\big)$$

jack1 · Answer

yeah... more like into either the polar equivalent or the phazor
polar equiv is the form:   2.1 (angle) 22.6 degrees
phazor splits it into real and imag, like the 2 sides of a triangle forming the hypotenuse
so form ______ (real)  + _______ i   (imaginary)

jack1 · Answer

so like a complex conjugate of it based on the frequency

jack1 · Answer

@UnkleRhaukus what you've put is more like the exact voltage in relation to time

jack1 · Answer

all good guys, i think it's an rms value so will just make some assumptions to justify me answer, cheers for the help tho

rsadhvika · Answer

2.1 is rms equivalent of 3 ?

rsadhvika · Answer

when we specify an ac voltage, we specify rms value itself. so why do we convert again ?

jack1 · Answer

@rsadhvika no, sorry, that was just an example to demonstrate the form of a complex conjugate/ phazor i was after, not an exact answer . 
2.1, 2.7 and 22.6 degrees were all just random numbers i threw out there, not actual values calculated

jack1 · Answer

so for the source voltage i just assumed it's complex... whatever... was 
3 + 0i
and calculated from there, it seemed to work out in the nodal analysis eqns as pretty close to the measured values in the lab, so... will have to study up some more, but fluked this one in ;)

rsadhvika · Answer

ohk.. these ive studied long back. dont remember a thing now... looks we loose frequency info in phasors or polar or rectangular form...  only phase we represent using imaginary component i guess