Implement exercise complex-numbers

config.json

@@ -823,6 +823,17 @@
             "control-flow (loops)"
       ]
     },
+    {
+      "uuid": "7f4d5743-7ab8-42ca-b393-767f7e9a4e97",
+      "slug": "complex-numbers",
+      "core": false,
+      "unlocked_by": "leap",
+      "difficulty": 6,
+      "topics": [
+        "Tuples",
+        "Mathematics"
+      ]
+    },
     {
       "uuid": "e7351e8e-d3ff-4621-b818-cd55cf05bffd",
       "slug": "accumulate",

exercises/complex-numbers/README.md

@@ -0,0 +1,22 @@
+# Complex Numbers
+
+A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+
+Assume the programming language you are using does not have an implementation of complex numbers.
+
+### Submitting Exercises
+
+Note that, when trying to submit an exercise, make sure the solution is in the `exercism/python/<exerciseName>` directory.
+
+For example, if you're submitting `bob.py` for the Bob exercise, the submit command would be something like `exercism submit <path_to_exercism_dir>/python/bob/bob.py`.
+
+
+For more detailed information about running tests, code style and linting,
+please see the [help page](http://exercism.io/languages/python).
+
+## Source
+
+Wikipedia [https://en.wikipedia.org/wiki/Complex_number](https://en.wikipedia.org/wiki/Complex_number)
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others have completed the exercise.

exercises/complex-numbers/complex_numbers.py

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+class ComplexNumber(object):
+    def __init__(self):
+        pass

exercises/complex-numbers/complex_numbers_test.py

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+import unittest
+
+import math
+
+from complex_numbers import ComplexNumber
+
+
+class ComplexNumbersTest(unittest.TestCase):
+
+    def test_real_part_of_a_purely_real_number(self):
+        input_number = ComplexNumber(1, 0)
+        self.assertEqual(input_number.real, 1)
+
+    def test_real_part_of_a_purely_imaginary_number(self):
+        input_number = ComplexNumber(0, 1)
+        self.assertEqual(input_number.real, 0)
+
+    def test_real_part_of_a_number_with_real_and_imaginary_part(self):
+        input_number = ComplexNumber(1, 2)
+        self.assertEqual(input_number.real, 1)
+
+    def test_imaginary_part_of_a_purely_real_number(self):
+        input_number = ComplexNumber(1, 0)
+        self.assertEqual(input_number.imaginary, 0)
+
+    def test_imaginary_part_of_a_purely_imaginary_number(self):
+        input_number = ComplexNumber(0, 1)
+        self.assertEqual(input_number.imaginary, 1)
+
+    def test_maginary_part_of_a_number_with_real_and_imaginary_part(self):
+        input_number = ComplexNumber(1, 2)
+        self.assertEqual(input_number.imaginary, 2)
+
+    def test_add_purely_real_numbers(self):
+        first_input = ComplexNumber(1, 0)
+        second_input = ComplexNumber(3, 0)
+        self.assertEqual(first_input.add(second_input).real, 4)
+        self.assertEqual(first_input.add(second_input).imaginary, 0)
+
+    def test_add_purely_imaginary_numbers(self):
+        first_input = ComplexNumber(0, 1)
+        second_input = ComplexNumber(0, 3)
+        self.assertEqual(first_input.add(second_input).real, 0)
+        self.assertEqual(first_input.add(second_input).imaginary, 4)
+
+    def test_add_numbers_with_real_and_imaginary_part(self):
+        first_input = ComplexNumber(1, 2)
+        second_input = ComplexNumber(4, 6)
+        self.assertEqual(first_input.add(second_input).real, 5)
+        self.assertEqual(first_input.add(second_input).imaginary, 8)
+
+    def test_subtract_purely_real_numbers(self):
+        first_input = ComplexNumber(1, 0)
+        second_input = ComplexNumber(-1, 0)
+        self.assertEqual(first_input.sub(second_input).real, 2)
+        self.assertEqual(first_input.sub(second_input).imaginary, 0)
+
+    def test_substract_numbers_with_real_and_imaginary_part(self):
+        first_input = ComplexNumber(1, 2)
+        second_input = ComplexNumber(-2, -2)
+        self.assertEqual(first_input.sub(second_input).real, 3)
+        self.assertEqual(first_input.sub(second_input).imaginary, 4)
+
+    def test_multiply_purely_real_numbers(self):
+        first_input = ComplexNumber(1, 0)
+        second_input = ComplexNumber(2, 0)
+        self.assertEqual(first_input.mul(second_input).real, 2)
+        self.assertEqual(first_input.mul(second_input).imaginary, 0)
+
+    def test_multiply_numbers_with_real_and_imaginary_part(self):
+        first_input = ComplexNumber(1, 2)
+        second_input = ComplexNumber(-5, 10)
+        self.assertEqual(first_input.mul(second_input).real, -5)
+        self.assertEqual(first_input.mul(second_input).imaginary, 20)
+
+    def test_divide_purely_real_numbers(self):
+        input_number = ComplexNumber(1.0, 0.0)
+        expected = ComplexNumber(0.5, 0.0)
+        divider = ComplexNumber(2.0, 0.0)
+        self.assertEqual(expected.real, input_number.div(divider).real)
+        self.assertEqual(expected.imaginary,
+                         input_number.div(divider).imaginary)
+
+    def test_divide_purely_imaginary_numbers(self):
+        input_number = ComplexNumber(0, 1)
+        expected = ComplexNumber(0.5, 0)
+        divider = ComplexNumber(0, 2)
+        self.assertEqual(expected.real, input_number.div(divider).real)
+        self.assertEqual(expected.imaginary,
+                         input_number.div(divider).imaginary)
+
+    def test_divide_numbers_with_real_and_imaginary_part(self):
+        input_number = ComplexNumber(1, 2)
+        expected = ComplexNumber(0.44, 0.08)
+        divider = ComplexNumber(3, 4)
+        self.assertEqual(expected.real, input_number.div(divider).real)
+        self.assertEqual(expected.imaginary,
+                         input_number.div(divider).imaginary)
+
+    def test_absolute_value_of_a_positive_purely_real_number(self):
+        self.assertEqual(ComplexNumber(5, 0).abs(), 5)
+
+    def test_absolute_value_of_a_negative_purely_real_number(self):
+        self.assertEqual(ComplexNumber(-5, 0).abs(), 5)
+
+    def test_absolute_value_of_imaginary_number_negative_imaginary_part(self):
+        self.assertEqual(ComplexNumber(0, -5).abs(), 5)
+
+    def test_absolute_value_of_imaginary_number_positive_imaginary_part(self):
+        self.assertEqual(ComplexNumber(0, 5).abs(), 5)
+
+    def test_absolute_value_of_a_number_with_real_and_imaginary_part(self):
+        self.assertEqual(ComplexNumber(3, 4).abs(), 5)
+
+    def test_conjugate_a_purely_real_number(self):
+        input_number = ComplexNumber(5, 0)
+        expected = ComplexNumber(5, 0)
+        self.assertEqual(expected.real, input_number.conjugate().real)
+        self.assertEqual(expected.imaginary,
+                         input_number.conjugate().imaginary)
+
+    def test_conjugate_a_purely_imaginary_number(self):
+        input_number = ComplexNumber(0, 5)
+        expected = ComplexNumber(0, -5)
+        self.assertEqual(expected.real, input_number.conjugate().real)
+        self.assertEqual(expected.imaginary,
+                         input_number.conjugate().imaginary)
+
+    def conjugate_a_number_with_real_and_imaginary_part(self):
+        input_number = ComplexNumber(1, 1)
+        expected = ComplexNumber(1, -1)
+        self.assertEqual(expected.real, input_number.conjugate().real)
+        self.assertEqual(expected.imaginary,
+                         input_number.conjugate().imaginary)
+
+    def test_eulers_identity_formula(self):
+        input_number = ComplexNumber(0, math.pi)
+        expected = ComplexNumber(-1, 0)
+        self.assertEqual(expected.real, input_number.exp().real)
+        self.assertEqual(expected.imaginary, input_number.exp().imaginary)
+
+    def test_exponential_of_0(self):
+        input_number = ComplexNumber(0, 0)
+        expected = ComplexNumber(1, 0)
+        self.assertEqual(expected.real, input_number.exp().real)
+        self.assertEqual(expected.imaginary, input_number.exp().imaginary)
+
+    def test_exponential_of_a_purely_real_number(self):
+        input_number = ComplexNumber(1, 0)
+        expected = ComplexNumber(math.e, 0)
+        self.assertEqual(expected.real, input_number.exp().real)
+        self.assertEqual(expected.imaginary, input_number.exp().imaginary)
+
+
+if __name__ == '__main__':
+    unittest.main()

exercises/complex-numbers/example.py

@@ -0,0 +1,42 @@
+import math
+
+
+class ComplexNumber(object):
+    def __init__(self, real, imaginary):
+        self.real = real
+        self.imaginary = imaginary
+
+    def add(self, other):
+        r = self.real + other.real
+        i = self.imaginary + other.imaginary
+        return ComplexNumber(r, i)
+
+    def mul(self, other):
+        r = self.real * other.real
+        i = self.imaginary * other.imaginary
+        return ComplexNumber(r, i)
+
+    def sub(self, other):
+        r = self.real - other.real
+        i = self.imaginary - other.imaginary
+        return ComplexNumber(r, i)
+
+    def div(self, other):
+        d = other.real * other.real + other.imaginary * other.imaginary
+        r = (self.real * other.real + self.imaginary *
+             other.imaginary) / float(d)
+        i = (self.imaginary * other.real - self.real *
+             self.real * other.imaginary) / float(d)
+        return ComplexNumber(r, i)
+
+    def abs(self):
+        square_sum = self.real * self.real + self.imaginary * self.imaginary
+        return math.sqrt(square_sum)
+
+    def conjugate(self):
+        return ComplexNumber(self.real, -1 * self.imaginary)
+
+    def exp(self):
+        r = round(math.cos(self.imaginary), 8) * math.exp(self.real)
+        i = round(math.sin(self.imaginary), 8) * math.exp(self.real)
+        return ComplexNumber(r, i)