The discussion revolves around the simplification of expressions involving complex numbers, specifically the square root of (n*i). Participants are exploring concepts related to complex analysis and the properties of analytical functions without relying on the Cauchy-Riemann equations.
The conversation is ongoing, with some participants providing insights into the relationships between variables and the nature of square roots in complex analysis. There is a recognition of the need for clearer questions to facilitate understanding, and some guidance has been offered regarding the interpretation of derivatives in this context.
There are references to external images that may contain examples or illustrations relevant to the discussion, but the specific content of these images is not described. The original poster's question appears to lack clarity, which has led to some confusion among participants.
m_s_a said:[url=http://www.up07.com/up7][PLAIN]http://www.up07.com/up7/uploads/a8bbd62a7c.jpg[/url]
http://www.up07.com/up7/uploads/f733271dae.jpg
m_s_a said:[url=http://www.up07.com/up7][PLAIN]http://www.up07.com/up7/uploads/5f965970a0.jpg[/url][/PLAIN]
Dick said:Yes. It's general. d/d(zbar)=0 is the same thing as saying i*d/dx=d/dy using the chain rule for partial derivatives. If you apply that to f=u(x,y)+i*v(x,y) you get the Cauchy-Riemann equations.
Dick said:Basically ok. (n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2). Recheck the sqrt(5i). But remember to be careful how you define 'sqrt' or remember that every nonzero number has two different square roots.