Page 24 - Calculus with Complex Numbers
P. 24
Ffgure 2./
Ffg ure 2.2
a w-plane, andthen indicate how geometrical ligures inthe z-plane are transformed
to geometrical ligures in the w-plane under the action of the function w = f (z).
For example, for the complex function w = .:2 we find that the grid lines
.x = corlstant y = constant in the z-plane transform to confocal parabolas in the
w-plane (Figtlre 2.2).
To see this observe that if z = .x + iy, w = u + i t? then
u + iv = (x + ïy)2 = .x2 - ),2 + zj-xy,
therefore
Lf 2 2
= . Y - #
