one can calculate a current I = Sqrt(P/R) = Sqrt(1000/6.55) = 12.35 Amps.
Correct.
You have used the RESISTIVE (R) part of the impedance to calculate the power.
Note that the REACTIVE (X) part of the impedance does not dissipate power.
Where |Z| = Sqrt( R^2 + X^2) = 88.15Ω.
Correct, assuming that the resistance and the reactance are in series.
one may calculate V as V = I*|Z| = 12.35 *88.15 = 1089Volts.
Correct.
This is the voltage across the resistive and reactive part of the impedance.
why a result from V= Sqrt(P*|Z|) is different from V = I*|Z| V = I*|Z| ? which one is correct in principle?
Both are correct in their own way !
The problem is your lack of understanding of resistive and reactive circuits.
V= Sqrt(P*|Z|) = Sqrt(88.15*1000) = 296Volts
Wrong.
You have a series circuit, the same current (12.35 Amps) flows through both the resistive and reactive part of the impedance.
For the "resistor"
V = I x R = 12.35 x 6.55 = 80.3 volts.
For the "reactor"
V = I x X = 12.35 x 87.906 = 1085.6 volts.
To find the total voltage, we cannot simply add 80.3 + 1085.6 = xxxx,
This is not correct because the voltages are 90 degrees out of phase with each other.
We must do:
V = sqrt ( 80.3 x 80.3 + 1085.6 x 1085.6) = 1088.6v (near enough the 1089v which was calculated earlier)
I hope that this makes sense to you.
JimB