Give a geometric description of the transformation w =A(z+B) where A and B are complex
constants and A is not equal to 0
Solution
let z=x+iy.now consider the transformation in two steps.
let B=k+il
z+B=p=x+k+i(y+l)...(1)
in other words x becomes x+k and y becomes y+l.hence the first transformation translates the
given curve by k units to the left and by l units down.
let A=Rei and z+B=rei
A(z+B)=Rrei(+)...(2)
Hence z+B is now rotated by an angle and magnified by R units by the second transformation.
So,the given transformation can be geometrically interpreted as translation,rotation and
magnification of the curve given by z.
give rating please....
Give a geometric description of the transformation w =A(z+B) where A.pdf
1. Give a geometric description of the transformation w =A(z+B) where A and B are complex
constants and A is not equal to 0
Solution
let z=x+iy.now consider the transformation in two steps.
let B=k+il
z+B=p=x+k+i(y+l)...(1)
in other words x becomes x+k and y becomes y+l.hence the first transformation translates the
given curve by k units to the left and by l units down.
let A=Rei and z+B=rei
A(z+B)=Rrei(+)...(2)
Hence z+B is now rotated by an angle and magnified by R units by the second transformation.
So,the given transformation can be geometrically interpreted as translation,rotation and
magnification of the curve given by z.
give rating please...
