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My problem is that I have multiple complex number in trigonometric form and I want to add those and get the magnitude of the result.

I am aware that the normal route would be to calculate the rectangular form, add the numbers and then I can easily calculate the magnitude.

I also know the trick, where you factor out the mean of the argument of two complex numbers like this:

$$\exp(4i) + \exp(6i) = \exp(5i) * (\exp(-i) + \exp(i)) = 2*\cos(1)*\exp(5i)$$

where you can easily read off the magnitude. But this does not work if I have to add more than two numbers. Does anyone know a trick for that?

Thanks

choco_addicted
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Kilsen
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    That's a nice trick, +1 for it. But, I doubt that there is anything to do in general other than the "normal route". – Lee Mosher Feb 06 '16 at 15:01
  • You can do this a pair of numbers at a time. Beware of numerical instabilities (adding approximately opposite numbers gives large relative errors) – vonbrand Feb 10 '16 at 01:12

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