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Perhaps it's Euler's Theorem that you're asking about. Euler's Theorem does not deal with complex numbers, but Euler's Formula does:
eiθ = cos(θ) + i*sin(θ). Where θ is measured in radians.
theorem
That is a theorem.A theorem.
Yes, it is a property of homogeneous function.
There is a beautiful proof of Euler's Therom, using the area of the sphere and spherical geometry.