About complex power

Network Theory
#1

Why do we consider ‘I’ as conjugate? What is its necessity?please elaborate in brief

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#2

When you multiply two complex quantities in polar form, their magnitude gets multiplied but the angles are added.
If you don’t consider conjugate see what happens,

                               S = V∠θv I∠θi

Where, V and I are in polar forms.

                               S = VI∠(θv+θi)

If you convert polar form into rectangular form

                               S = VI Cos(θv+θi) + i VI Sin(θv+θi)
                               S = P + iQ

P = VI Cos(θv+θi) which is not what we wanted and it is not equal to the one we’ve learned earlier.
To way around this we use conjugate operation in S = VI* to make (θv-θi).

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#3

Thank you for your explanation