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Let us assume that we have $f:\mathbb{R} \to \mathbb{R}$. Also let us assume that $x_1\in \mathbb{R}$ and $x_2\in \mathbb{R}$ are given too. With this we can calculate $y_1 = f(x_1)$ and $y_2 = f(x_2)$.

Now if we want to interpolate/extrapolate an in-between value we could take a value like e.g. $\alpha \in \mathbb{R}$ (but for interpolation $\alpha$ would be in range $[0,1]$).

With this we could calculate the interpolated values $x_{irp},y_{irp} \in \mathbb{R}$ like:

$$x_{irp}=\alpha \cdot x_1 + (1- \alpha) \cdot x_2$$ $$y_{irp}=\alpha \cdot y_1 + (1- \alpha) \cdot y_2$$

Now my question:

Does the same approach also works for complex numbers too? In this case instead of $\mathbb{R}$ we would have $\mathbb{C}$.

(I know indeed that for multidimensional input and output this approach works, but for complex numbers too?)

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Yes, exactly the same method will work (with exactly the same limitations that this is a really bad estimate in general).

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  • $\begingroup$ Is there a better approach too? I mean like for the $\mathbb{R}$ numbers with a square line approximation? How would this one work for $\mathbb{C}$? $\endgroup$ – PiMathCLanguage Nov 26 '18 at 13:51

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