D.B. Amuda  , O.M. Oni  , A.O. Awodugba  , 
    Conjugate Polar Form of Cauchy-Riemann Equations,
    Research Journal of Applied Sciences,
    Volume 2,Issue 9,
    2007,
    Pages 994-997,
    ISSN 1815-932x,
    rjasci.2007.994.997,
    (https://makhillpublications.co/view-article.php?doi=rjasci.2007.994.997)
    Abstract: If we use the form z = (cos  + I sin ) and set f(z) = f (re<SUP>i </SUP>) = u(r,  ) + iv(r,  ), then the Cauuchy-Riemann equations are<IMG SRC=http://www.medwelljournals.com/fulltext/rjas/2007/Image24.gif/Image23.gif>


In this study, we establish the conjugate forms of the above Cauchy-Riemann differential equations in polar coordinate. That  is;  if  we  use  the  conjugate  polar form <IMG SRC=http://www.medwelljournals.com/fulltext/rjas/2007/Image24.gif>
 =r (cos  + I sin ) and set f(<IMG SRC=http://www.medwelljournals.com/fulltext/rjas/2007/Image24.gif>
) = f (re<SUP>-i </SUP>) = u(r,  ) + iv(r, - ), then the conjugate polar form Cauuchy-Riemann equations are
<IMG SRC=http://www.medwelljournals.com/fulltext/rjas/2007/Image25.gif>
which is a `reflection` of Cauchy-Riemann Differential Equations in Polar coordinate.
    Keywords: Analyticity;Cauchy-Riemann;conjugate;polar;reflection