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# 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. ## 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.
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