Complex Fibonacci numbers
Wolfram Language (Mathematica), 30 bytes
(h=2/--√5;h^#-(1-h)^#)√.2&amp;

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Uses \$\frac{\sqrt 5+1}{2}=\frac{2}{\sqrt 5-1}\$. Mathematica's pre-increment/decrement operators still return the desired value when used on (non-variable) non-atoms.
The built-in Fibonacci is a continuous real function, the real part of the Binet formula: \$F_n=\frac{\phi^n-\cos(\pi n)\phi^{-n}}{\sqrt 5}\$.