

'''simple docstring'''





import cmath
import math






def 					lowerCamelCase_     (							UpperCAmelCase_							:     float							,       UpperCAmelCase_							:     float							,       UpperCAmelCase_							:     float							,       UpperCAmelCase_							:     float	)						->				complex:




	'''simple docstring'''




	_UpperCamelCase   :		Dict			=						math.radians(UpperCAmelCase_	)
	_UpperCamelCase   :		Tuple			=						math.radians(UpperCAmelCase_	)

	# Convert voltage and current to rectangular form
	_UpperCamelCase   :		Dict			=						cmath.rect(UpperCAmelCase_							,       UpperCAmelCase_	)
	_UpperCamelCase   :		Union[str, Any]			=						cmath.rect(UpperCAmelCase_							,       UpperCAmelCase_	)

	# Calculate apparent power
	return voltage_rect * current_rect


if __name__ == "__main__":
							import doctest

							doctest.testmod()







from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
lowerCAmelCase__								=		numpy.array([0, 0])
lowerCAmelCase__								=		numpy.array([0.5, 0.8_66_02_54])
lowerCAmelCase__								=		numpy.array([1, 0])
lowerCAmelCase__								=		[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]






def 					lowerCamelCase_     (							UpperCAmelCase_							:     list[numpy.ndarray]							,       UpperCAmelCase_							:     int	)						->				list[numpy.ndarray]:




	'''simple docstring'''




	_UpperCamelCase   :		Tuple			=						initial_vectors
	for _ in range(UpperCAmelCase_	):
		_UpperCamelCase   :		str			=						iteration_step(UpperCAmelCase_	)
	return vectors






def 					lowerCamelCase_     (							UpperCAmelCase_							:     list[numpy.ndarray]	)						->				list[numpy.ndarray]:




	'''simple docstring'''




	_UpperCamelCase   :		int			=						[]
	for i, start_vector in enumerate(vectors[:-1]	):
		_UpperCamelCase   :		Union[str, Any]			=						vectors[i + 1]
		new_vectors.append(UpperCAmelCase_	)
		_UpperCamelCase   :		Tuple			=						end_vector - start_vector
		new_vectors.append(start_vector + difference_vector / 3	)
		new_vectors.append(
		    start_vector + difference_vector / 3 + rotate(difference_vector / 3							,       6_0	)	)
		new_vectors.append(start_vector + difference_vector * 2 / 3	)
	new_vectors.append(vectors[-1]	)
	return new_vectors






def 					lowerCamelCase_     (							UpperCAmelCase_							:     numpy.ndarray							,       UpperCAmelCase_							:     float	)						->				numpy.ndarray:




	'''simple docstring'''




	_UpperCamelCase   :		str			=						numpy.radians(UpperCAmelCase_	)
	_UpperCamelCase	,		_UpperCamelCase   :		Optional[Any]			=						numpy.cos(UpperCAmelCase_	), numpy.sin(UpperCAmelCase_	)
	_UpperCamelCase   :		Any			=						numpy.array(((c, -s), (s, c))	)
	return numpy.dot(UpperCAmelCase_							,       UpperCAmelCase_	)






def 					lowerCamelCase_     (							UpperCAmelCase_							:     list[numpy.ndarray]	)						->				None:




	'''simple docstring'''




	_UpperCamelCase   :		str			=						plt.gca()
	axes.set_aspect('equal'	)

	# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
	# y-coordinates as inputs, which are constructed from the vector-list using
	# zip()
	_UpperCamelCase	,		_UpperCamelCase   :		Dict			=						zip(*UpperCAmelCase_	)
	plt.plot(UpperCAmelCase_							,       UpperCAmelCase_	)
	plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							lowerCAmelCase__								=		iterate(INITIAL_VECTORS, 5)
							plot(processed_vectors)




