On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 22
amp;) (z - 2n) = 0 vanishes if the product of a0 and two linear factors, vanishes; for example, if aQ ( z - z1) (z - z2) ■ a0zV«7:+a.2 = (a0 + ib0)(x +iy)8 + (ax + i *j)(x + i y ) + a2 + i b2 = 0. (X)Equating the real and imaginary parts:-u = a0 x2 - a0 y2 - 2 h0 x y + ax x - y + a2 = 0. v = b0 x2… … -NJ-0 Fig. II. u a0 + bQ v = (a0 2 + b0 2)(x2 - ya) + (a! a0 + b0 bx) x - (*0 bx - a2 b0) y + ao a2 + *o *2 = °- (11) 0 Dividing (11) by a0a + b02 and placing it in the form( + aia0 + bob, ) 8- / + a0^i - ajbp V1 / aia0 + b,b 1 2 (ao8 + b0*)J t 2 UoS + W I2 <V + *o aO*l ai*Q a0a2 + *0*2 , 0 + 2…
