Complex numbers operations: sum, mul, abs

maths/complex/abs.py

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+from math import sqrt
+
+from complex import Complex
+
+
+def complex_abs(c: Complex) -> float:
+    """
+    Computes the absolute value of a complex number.
+    The result is a non-negative real number, that represents the lenght
+    of the vector (real_part, imaginary_part) in R².
+    >>> c = Complex(-3, 4)
+    >>> complex_abs(c)
+    5.0
+    """
+    return sqrt(c.real_part ** 2 + c.imaginary_part ** 2)

maths/complex/complex.py

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+"""
+Complex number implementation.
+
+Definition:
+    A complex number is an ordered pair of real numbers (a, b). The first
+    component, a, is called the real part; the second component, b, is called
+    the imaginary part.
+"""
+
+
+class Complex:
+    def __init__(self, real_part: float, imaginary_part: float):
+        """
+        Both a and b are real numbers (float in Python).
+        """
+        self.real_part = real_part
+        self.imaginary_part = imaginary_part
+
+    def __repr__(self) -> str:
+        """
+        Represent the complex number as a 2-tuple.
+        """
+        return (self.real_part, self.imaginary_part)

maths/complex/mul.py

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+from complex import Complex
+
+
+def complex_mul(a: Complex, b: Complex) -> Complex:
+    """
+    Multiplicate two complex numbers and return the result.
+    >>> a = Complex(0, 1)
+    >>> b = Complex(0, 1)
+    >>> c = complex_mul(a, b)
+    >>> c.__repr__()
+    (-1, 0)
+    """
+    return Complex(
+        a.real_part * b.real_part - a.imaginary_part * b.imaginary_part,
+        a.real_part * b.imaginary_part + b.real_part * a.imaginary_part,
+    )

maths/complex/sum.py

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+from complex import Complex
+
+
+def complex_sum(a: Complex, b: Complex) -> Complex:
+    """
+    Add two complex numbers and return the result.
+    >>> a = Complex(1, 2)
+    >>> b = Complex(0, -1)
+    >>> c = complex_sum(a, b)
+    >>> c.__repr__()
+    (1, 1)
+    """
+    return Complex(a.real_part + b.real_part, a.imaginary_part + b.imaginary_part)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()