Finding a derivative with imaginary numbers?

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If I have some function $f = (1 + 7i - x)(7 + 5i - x)(3 + 1i - x)$

How do I find its derivative? I know it is $(13/3 + 11i/3 - x)(3 + 5i - x)$ but I don't know how to find it.

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1 Answer

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Expand the function $f$:

$$f(x) = -x^3+(11+13i)x^2+(16-98i)x-138+134i.$$ Then differentiate as usual.

Factoring the derivative gives:

$$f'(x) = (3+5i-x)(3x-13-11i).$$

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