Complex Power Q: Solved w/ My Friend & I

[A.J.710]

Homework Statement

[moderator note: Image inserted to be visible in problem statement]

Homework Equations

The Attempt at a Solution

My friend and I are trying to figure out how this works. This is the questions and the solution manual. We understand where the real power comes from but not at all how to get the complex. If anyone could give a brief explanation, that would be great. Preferably A because that's where we started and just cannot get the complex part at all.[/B]

 

[NascentOxygen]

Active, reactive, and apparent power. It's well explained on Wikipedia.

They form a right-angle triangle: active or real power on the base, reactive power on the altitude, and complex power forms the hypotenuse. One of the angles is the power factor angle such that P = S.cos Φ