TY  - JOUR
T1  - Conjugate Polar Form of Cauchy-Riemann Equations
AU - , D.B. Amuda AU - , O.M. Oni AU - , A.O. Awodugba 
JO  - Research Journal of Applied Sciences
VL  - 2
IS  - 9
SP  - 994
EP  - 997
PY  - 2007
DA  - 2001/08/19
SN  - 1815-932x
DO  - rjasci.2007.994.997
UR  - https://makhillpublications.co/view-article.php?doi=rjasci.2007.994.997
KW  - Analyticity
KW  -Cauchy-Riemann
KW  -conjugate
KW  -polar
KW  -reflection
AB  - 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.
ER  -