"""simple docstring"""
from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray





def 				lowerCAmelCase__      (     _UpperCamelCase    :			float	,     _UpperCamelCase    :			float	,     _UpperCamelCase    :			bool = False   )   ->			list[float]:





      """simple docstring"""






      if radian_mode:
            return [magnitude * cos(_UpperCamelCase   ), magnitude * sin(_UpperCamelCase   )]
      return [magnitude * cos(radians(_UpperCamelCase   )   ), magnitude * sin(radians(_UpperCamelCase   )   )]





def 				lowerCAmelCase__      (     _UpperCamelCase    :			NDArray[floataa]	,     _UpperCamelCase    :			NDArray[floataa]	,     _UpperCamelCase    :			float = 1_0**-1   )   ->			bool:





      """simple docstring"""






      snake_case        =     cross(_UpperCamelCase	,     _UpperCamelCase   )
      snake_case        =     sum(_UpperCamelCase   )
      return abs(_UpperCamelCase   ) < eps


if __name__ == "__main__":
     # Test to check if it works
     SCREAMING_SNAKE_CASE__   =					array(
         [
             polar_force(718.4, 180 - 30),
             polar_force(879.54, 45),
             polar_force(100, -90),
         ]
     )

     SCREAMING_SNAKE_CASE__   =					array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem 1 in image_data/2D_problems.jpg
     SCREAMING_SNAKE_CASE__   =					array(
         [
             polar_force(30 * 9.81, 15),
             polar_force(215, 180 - 45),
             polar_force(264, 90 - 30),
         ]
     )

     SCREAMING_SNAKE_CASE__   =					array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem in image_data/2D_problems_1.jpg
     SCREAMING_SNAKE_CASE__   =					array([[0, -2_000], [0, -1_200], [0, 15_600], [0, -12_400]])

     SCREAMING_SNAKE_CASE__   =					array([[0, 0], [6, 0], [10, 0], [12, 0]])

     assert in_static_equilibrium(forces, location)

     import doctest

     doctest.testmod()



"""simple docstring"""
import cmath
import math





def 				lowerCAmelCase__      (     _UpperCamelCase    :			float	,     _UpperCamelCase    :			float	,     _UpperCamelCase    :			float	,     _UpperCamelCase    :			float   )   ->			complex:





						"""simple docstring"""






						snake_case        =     math.radians(_UpperCamelCase   )
						snake_case        =     math.radians(_UpperCamelCase   )

						# Convert voltage and current to rectangular form
						snake_case        =     cmath.rect(_UpperCamelCase	,     _UpperCamelCase   )
						snake_case        =     cmath.rect(_UpperCamelCase	,     _UpperCamelCase   )

						# Calculate apparent power
						return voltage_rect * current_rect


if __name__ == "__main__":
					import doctest

					doctest.testmod()


