Understanding Complex Power Calculations: Why is S = 1/2 * V * I?

[arkturus]

I don't have a question about a specific HW problem, just a general questions.

When calculating complex power, I understand it's S = Veff*Ieff(conjugate). However, S can also be calculate as S = 1/2 * V * I. Why is this? I feel I'm missing something simple, but I'm pretty lost because the current chapter in circuit theory has a bunch of definitions.

 

[Zryn]

When you say S = Veff*Ieff(conjugate), what does the 'eff' stand for, and what is the difference between Veff and V, or Ieff and I?

Veff * Ieff = V/<something> * I/<something> = VI / <something>^2 ...

 

[arkturus]

Ah thanks, simple enough. VeffIeff = V/sqrt(2) * I/sqrt(2) which simplifies to VI/2. Much appreciated.