InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Show that the equaton of any circle in the complex plane is of the form z barz+b bar z+ b bar z+c=0,( b in C, c in R) |
|
Answer» Solution :Assume the genral FRORM of the equation of a circle in cartesion co-ordinates as `x^(2)+y^(2)2ag+2fy+c=0` `(g , f in R)""..(1)` To write this equation in the complex VARIABLE formlet `(x,y)=Z` Then `(z+ BAR z)/(2)= x, (z- bar z)/(2 i)` `=y=(-i (z bar z))/(2)` `:.x^(2)+y^(2)=|z|^(2)=z barz` Substituting these,RESULTING in equation (1), we obtain `z bar z+g(z+barz)+f(z- barz)(-i)+c=0` i.e., `z bar z+(g- if)z+ (g+ if) bar z+c=0 "" (2)` If `(g+if)=b` , then equation (2) can be writenas `z bar z+ bar b z+b bar z+c=0` |
|