z = h(x) + ig(x)(adsbygoogle = window.adsbygoogle || []).push({});

True or False: By the definition of the complex plane, h(x) and ig(x) will always be orthogonal.

If this was true, wouldn't that mean that we can find a 'very general' Fourier series representation of any function f(x) as an infinite series of An*h(x) + infinite series of Bn*ig(x) ?. I am aware that finding a Fourier series representation of f(x) doesn't mean that it will converge, and if it does converge, it won't necessary converge to f(x).

for example h(x) = x^2 , g(x) = ln(x)

Sorry if this is a stupid question, I'm just trying to understand some stuff...

Thanks.

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# Do all complex functions have orthogonal real and imaginary parts?

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