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@@ -0,0 +1,158 @@
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+import math
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+
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+class complex:
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+ def __init__(self, real, imag=0):
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+ self._real = float(real)
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+ self._imag = float(imag)
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+
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+ @property
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+ def real(self):
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+ return self._real
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+
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+ @property
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+ def imag(self):
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+ return self._imag
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+
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+ def __repr__(self):
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+ return f"({self.real}+{self.imag}j)"
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+
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+ def __eq__(self, other):
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+ if type(other) is complex:
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+ return self.real == other.real and self.imag == other.imag
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+ if type(other) in (int, float):
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+ return self.real == other and self.imag == 0
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+ return NotImplemented
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+
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+ def __add__(self, other):
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+ if type(other) is complex:
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+ return complex(self.real + other.real, self.imag + other.imag)
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+ if type(other) in (int, float):
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+ return complex(self.real + other, self.imag)
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+ return NotImplemented
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+
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+ def __radd__(self, other):
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+ return self.__add__(other)
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+
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+ def __sub__(self, other):
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+ if type(other) is complex:
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+ return complex(self.real - other.real, self.imag - other.imag)
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+ if type(other) in (int, float):
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+ return complex(self.real - other, self.imag)
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+ return NotImplemented
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+
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+ def __rsub__(self, other):
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+ if type(other) is complex:
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+ return complex(other.real - self.real, other.imag - self.imag)
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+ if type(other) in (int, float):
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+ return complex(other - self.real, -self.imag)
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+ return NotImplemented
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+
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+ def __mul__(self, other):
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+ if type(other) is complex:
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+ return complex(self.real * other.real - self.imag * other.imag,
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+ self.real * other.imag + self.imag * other.real)
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+ if type(other) in (int, float):
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+ return complex(self.real * other, self.imag * other)
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+ return NotImplemented
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+
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+ def __rmul__(self, other):
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+ return self.__mul__(other)
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+
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+ def __pow__(self, other: int | float):
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+ if type(other) in (int, float):
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+ return complex(self.__abs__() ** other * math.cos(other * phase(self)),
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+ self.__abs__() ** other * math.sin(other * phase(self)))
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+ return NotImplemented
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+
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+ def __abs__(self) -> float:
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+ return math.sqrt(self.real ** 2 + self.imag ** 2)
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+
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+
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+# Conversions to and from polar coordinates
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+
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+def phase(z: complex):
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+ return math.atan2(z.imag, z.real)
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+
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+def polar(z: complex):
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+ return z.__abs__(), phase(z)
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+
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+def rect(r: float, phi: float):
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+ return r * math.cos(phi) + r * math.sin(phi) * 1j
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+
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+# Power and logarithmic functions
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+
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+def exp(z: complex):
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+ return math.exp(z.real) * rect(1, z.imag)
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+
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+def log(z: complex, base=2.718281828459045):
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+ return math.log(z.__abs__(), base) + phase(z) * 1j
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+
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+def log10(z: complex):
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+ return log(z, 10)
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+
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+def sqrt(z: complex):
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+ return z ** 0.5
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+
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+# Trigonometric functions
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+
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+def acos(z: complex):
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+ return -1j * log(z + sqrt(z * z - 1))
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+
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+def asin(z: complex):
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+ return -1j * log(1j * z + sqrt(1 - z * z))
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+
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+def atan(z: complex):
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+ return 1j / 2 * log((1 - 1j * z) / (1 + 1j * z))
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+
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+def cos(z: complex):
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+ return (exp(z) + exp(-z)) / 2
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+
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+def sin(z: complex):
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+ return (exp(z) - exp(-z)) / (2 * 1j)
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+
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+def tan(z: complex):
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+ return sin(z) / cos(z)
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+
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+# Hyperbolic functions
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+
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+def acosh(z: complex):
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+ return log(z + sqrt(z * z - 1))
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+
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+def asinh(z: complex):
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+ return log(z + sqrt(z * z + 1))
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+
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+def atanh(z: complex):
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+ return 1 / 2 * log((1 + z) / (1 - z))
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+
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+def cosh(z: complex):
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+ return (exp(z) + exp(-z)) / 2
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+
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+def sinh(z: complex):
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+ return (exp(z) - exp(-z)) / 2
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+
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+def tanh(z: complex):
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+ return sinh(z) / cosh(z)
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+
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+# Classification functions
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+
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+def isfinite(z: complex):
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+ return math.isfinite(z.real) and math.isfinite(z.imag)
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+
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+def isinf(z: complex):
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+ return math.isinf(z.real) or math.isinf(z.imag)
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+
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+def isnan(z: complex):
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+ return math.isnan(z.real) or math.isnan(z.imag)
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+
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+def isclose(*args, **kwargs):
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+ raise NotImplementedError
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+
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+# Constants
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+
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+pi = math.pi
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+e = math.e
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+tau = 2 * pi
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+inf = math.inf
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+infj = complex(0, inf)
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+nan = math.nan
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+nanj = complex(0, nan)
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