A complex number is a number in the form a + b * i where a and b are real and i satisfies i^2 = -1.
a is called the real part and b is called the imaginary part of z.
The conjugate of the number a + b * i is the number a - b * i.
The absolute value of a complex number z = a + b * i is a real number |z| = sqrt(a^2 + b^2). The square of the absolute value |z|^2 is the result of multiplication of z by its complex conjugate.
The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
(a + i * b) + (c + i * d) = (a + c) + (b + d) * i,
(a + i * b) - (c + i * d) = (a - c) + (b - d) * i.
Multiplication result is by definition
(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i.
The reciprocal of a non-zero complex number is
1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i.
Dividing a complex number a + i * b by another c + i * d gives:
(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i.
Raising e to a complex exponent can be expressed as e^(a + i * b) = e^a * e^(i * b), the last term of which is given by Euler's formula e^(i * b) = cos(b) + i * sin(b).
Implement the following operations:
- addition, subtraction, multiplication and division of two complex numbers,
- conjugate, absolute value, exponent of a given complex number.
Assume the programming language you are using does not have an implementation of complex numbers.
Go through the setup instructions for Java to install the necessary dependencies:
https://exercism.io/tracks/java/installation
You can run all the tests for an exercise by entering the following in your terminal:
$ gradle testUse
gradlew.batif you're on Windows
In the test suites all tests but the first have been skipped.
Once you get a test passing, you can enable the next one by removing the
@Ignore("Remove to run test") annotation.
Wikipedia https://en.wikipedia.org/wiki/Complex_number
It's possible to submit an incomplete solution so you can see how others have completed the exercise.