Real and Reactive Power

p
```import math

def real_power(apparent_power: float, power_factor: float) -> float:
"""
Calculate real power from apparent power and power factor.

Examples:
>>> real_power(100, 0.9)
90.0
>>> real_power(0, 0.8)
0.0
>>> real_power(100, -0.9)
-90.0
"""
if (
not isinstance(power_factor, (int, float))
or power_factor < -1
or power_factor > 1
):
raise ValueError("power_factor must be a valid float value between -1 and 1.")
return apparent_power * power_factor

def reactive_power(apparent_power: float, power_factor: float) -> float:
"""
Calculate reactive power from apparent power and power factor.

Examples:
>>> reactive_power(100, 0.9)
43.58898943540673
>>> reactive_power(0, 0.8)
0.0
>>> reactive_power(100, -0.9)
43.58898943540673
"""
if (
not isinstance(power_factor, (int, float))
or power_factor < -1
or power_factor > 1
):
raise ValueError("power_factor must be a valid float value between -1 and 1.")
return apparent_power * math.sqrt(1 - power_factor**2)

if __name__ == "__main__":
import doctest

doctest.testmod()
```