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c++mathstlfftcomplex-numbers

Representation of complex numbers in C++ for Discrete Fourier Transformation

I am currently writing a small tool which should help me check whether my manually calculated fourier vectors are correct. Now i need the n-th Root of Unity specified by omega = exp(2*pi*i / n). Can somebody explain me how to represent this omega as a complex in C++?

Solution

  • Use Euler's formula:

    exp(2πi/n) = cos(2π/n) + i sin(2π/n)

    Then it's easy:

    complex<double> rootOfUnity(cos(TWOPI/n), sin(TWOPI/n));

    (replace TWOPI with either a macro available on your system or just the value of 2π however you see fit).