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(complex_1: Complex) -> float:
+    """
+    Computes the absolute value of a complex number.
+    The result is a non-negative real number, that represents the length
+    of the vector (real_part, imaginary_part) in R².
+    >>> complex_1 = Complex(-3, 4)
+    >>> complex_abs(complex_1)
+    5.0
+    """
+    return sqrt(complex_1.real_part ** 2 + complex_1.imaginary_part ** 2)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

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) -> None:
+        """
+        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.
+        >>> complex_1 = Complex(1, 2)
+        >>> complex_1.__repr__()
+        (1, 2)
+        """
+        return (self.real_part, self.imaginary_part)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/complex/mul.py

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+from complex import Complex
+
+
+def complex_mul(complex_1: Complex, complex_2: Complex) -> Complex:
+    """
+    Multiplicate two complex numbers and return the result.
+    >>> complex_1 = Complex(0, 1)
+    >>> complex_2 = Complex(0, 1)
+    >>> c = complex_mul(complex_1, complex_2)
+    >>> c.__repr__()
+    (-1, 0)
+    """
+    return Complex(
+        complex_1.real_part * complex_2.real_part
+        - complex_1.imaginary_part * complex_2.imaginary_part,
+        complex_1.real_part * complex_2.imaginary_part
+        + complex_2.real_part * complex_1.imaginary_part,
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/complex/sum.py

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+from complex import Complex
+
+
+def complex_sum(complex_1: Complex, complex_2: Complex) -> Complex:
+    """
+    Add two complex numbers and return the result.
+    >>> complex_1 = Complex(1, 2)
+    >>> complex_2 = Complex(0, -1)
+    >>> c = complex_sum(complex_1, complex_2)
+    >>> c.__repr__()
+    (1, 1)
+    """
+    return Complex(
+        complex_1.real_part + complex_2.real_part,
+        complex_1.imaginary_part + complex_2.imaginary_part,
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()