Rationalisation of a complex denominator
When deriving sums of trig series, does anyone have any suggestions about when to use the method of multiplication
of denominator by conjugate pair vs factorisation of e^ ((pi)i/2n)?
of denominator by conjugate pair vs factorisation of e^ ((pi)i/2n)?
Reply 1
It really comes down to what you’re working with. If it’s just a single fraction like 1/(a+bi), I’d just multiply by the conjugate because it’s quick and straightforward. But if you’re dealing with trig series, switching to the exponential form using e^(i*pi/2n) usually makes life easier. It turns the whole thing into a geometric series problem instead of having to rationalise every term by hand. For anything with a repeating or symmetric structure, the exponential approach just feels way more natural.
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