There are two types of planes in Mathematics.Real and Complex plane.In comppex plane z=x+iy and w= u+iv are two complex variables.If variables x,y traces out a curve in z plane then corrosponding u,v also traces out a curve in w plane. This functional relation between z and w is called Mapping.
Two types of Mapping
1) Conformal mapping
2) Isogonal mapping
W= z^2 is conformal mapping.in which straight lines always convert into parabola.
This tranaformation converts straight lines x = a of Z plane into parabolas on positive of u axis and coverts straight lines y=a into parabolas into negative of u axis..
This tranaform converts first quadrant of z plne into upper half of w plane and
Upper half of z plane into whole of the w plane..
