# Talk:Derivation of the Routh array

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## Comments

Isn't the left hand side of eqns 13 and 14 supposed to be only${\displaystyle \theta (x)}$ (no index ${\displaystyle r_{i}}$)? (Havresylt (talk) 05:45, 19 October 2009 (UTC))

Thanks! You are absolutely correct, too much copy-pasta. I've corrected it. --Zaxxonal (talk) 22:07, 6 March 2010 (UTC)

Equation (6) uses a formula for the argument of a complex number, that depends upon the complex number to have a positive real part. Note that the arguments of -0.001 + i and 0.001+i do not differ by pi as the formula would suggest! Equation (9) uses equation (6) on a complex number with a negative real part. The rest of the article builds upon this result, so this needs to be fixed. Mreiki (talk) 18:44, 12 February 2011 (UTC)

Sorry for my inadequate initial response, Mreiki. Perhaps it would be better if equation 6 merely stated tan(@) = IM{f(x)}/RE{f(x)}. Equation (9) is not evaluated on a complex number with a negative real part. Before evaluation, the negative sign is removed and applied to the limit, which can be done since tan([email protected]) = -tan(@).
Please also note that if you were to apply the atan2 function directly to the arguments shown in (9), (10), (11) and (12), instead of performing a limit substitution, you get the same results. For example, in (9), pi/2 + pi = 3pi/2 which is the same angle as -pi/2, in (10), -pi/2 - pi = -3pi/2 which is the same angle as pi/2. In (11) and (12), the arguments have positive real parts without substitution. Zaxxonal (talk) 06:43, 16 August 2011 (UTC)
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