Ooops sorry, bit of an obvious lack of clarity there, it should read
j*j = j[sup]2[/sup] = -1
How about some real clarity.
A general sinusoidal voltage can be written as:
*v = V[sub]m[/sub]*cos(wt+ø)
If w is known, you can assume a synchronous reference frame and use Steinmetz’s phasor notation.
In that case, the voltage is fully described by the two quantities :
V[sub]m[/sub] and ø.
It can be equivalently expressed as two orthogonal components in either rectangular or polar coordinates as:
V = V[sub]m[/sub](cos ø + j sin ø) = *V[sub]m[/sub]*e[sup]jø[/sup]
It’s the adoption of a synchronous reference frame that’s the critical step, casdave, not the use of complex numbers.
You often find that equations describing circuits are nonanalytic, i.e., are undifferentiable in complex form, so you’re prevented from using complex numbers in common situations. But you still use the synchronous reference frame, because it eliminates the wt from the equations.
Now my head hurts. I’ll read this again in 14 hours.
Thanks, Demostylus & Casdave…
You can have what`s called a “high leg” setup where one of the phases to ground is different than the rest. This is very uncommon but does exist in some cities. Typically an older service too. Do a search for “grounded B phase” or “high leg/wild leg” for examples of atypical services.
You can switch ANY two leads to reverse a three phase motor.
Desmostylus
I just took a look at some my old notes, and yes you are completely right, so right you could even have been one of my lecturers 
It surprises me that the use of trig and complex numbers came so early in the course, year one out of five.
I looked at some of the circular functions and they are just as horrible as I remember, with terms looking so very similar except for signs, or the use of terms for which I never did find a use.
I might just have a browse around, or maybe not, it certainly brings back memories of late nights, trains home arriving late, hurrying off to the student union bar between sessions etc.