Talk:Sum of Complex Numbers in Exponential Form

Perhaps better to use the multifunction $\tan^{-1}$ here rather than $\arctan$? --GFauxPas (talk) 22:14, 24 June 2014 (UTC)

Don't think so. We're only interested in the principal value. --prime mover (talk) 05:19, 25 June 2014 (UTC)

In the "General Result" section, the formula for the modulus ($r$) contains a term for the sum of the moduli of the complex numbers being added. Should this be the sum of the *squares* of the moduli, to be consistent with the formula for $r_3$ in the "Theorem" section? --R gayler (talk) 23:02, 20 August 2022 (UTC)

Probably. If you can find this result somewhere written as it is supposed to be, please share. This was a question set in an exercise in a text book. So very possibly wrong. --prime mover (talk) 23:37, 20 August 2022 (UTC)

I have spent a while searching the internet for a correct source. Formulae for addition of complex numbers in exponential form are rare and ProofWiki is the only place I have found a general formula for adding more than two complex numbers. My mathematical expertise is approximately zero and I don't have access to any books that are likely to mention the topic. FWIW I notice that the possibly wrong formula is imported from Sum of Complex Numbers in Exponential Form/General Result. Looking at the proof on that page, there is a line that says "$= {r_k}^2$ Sum of Squares of Sine and Cosine" but 3 lines lower in the conclusion ("Hence: $r = ...$") the squaring has been dropped. It looks to me like a simple oversight/typo. In the absence of a known correct external reference, perhaps someone with adequate mathematical expertise (i.e. not me) could correct that proof on the basis of their own expertise.--R gayler (talk) 01:28, 21 August 2022 (UTC)

Right this has been fixed. Thanks --prime mover (talk) 08:04, 21 August 2022 (UTC)

Excellent. Thank you. --R gayler (talk) 09:20, 21 August 2022 (UTC)