In this lesson, we will learn how to interpret möbius transformation in the complex plane.

Q1:

Consider the MΓΆbius transformations π(π§)=π§+3πππ§β2ο§ and π(π§)=ππ§+12π§ο¨, where π§β 2π or 0.

Write an expression for the composition πβπ(π§)ο§ο¨.

Q2:

A transformation that maps the π§-plane to the π€-plane is defined by πβΆπ§β¦1π§, where π§β 0.

Find an equation for the image of |π§|=2 under the transformation.

Find an equation for the image of arg(π§)=3π4.

Find a Cartesian equation for the image of Im(π§)=2.

Find a Cartesian equation for the image of |π§βπ|=12.

Q3:

A transformation that maps the π§-plane to the π€-plane is defined by πβΆπ§β¦13π§β6π.

Find the Cartesian equation for the image of |π§+2|=3.

Find the Cartesian equation for the image of Re(π§)=5.

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