JavaExercism/exercises/complex-numbers

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.

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.

Exponent of a complex number can be expressed as exp(a + i * b) = exp(a) * exp(i * b), and the last term is given by Euler's formula exp(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.

Running the tests

You can run all the tests for an exercise by entering

$ gradle test

in your terminal.

Source

Wikipedia 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.