3. Consider the function f(z) = 2eim/3z. The following sketch (a) Find the Cartesian form of 2e2"/3. (b) Let the unit sq

[answerhappygod]

3 Consider The Function F Z 2eim 3z The Following Sketch A Find The Cartesian Form Of 2e2 3 B Let The Unit Sq 1 (45.37 KiB) Viewed 21 times

3. Consider the function f(z) = 2eim/3z. The following sketch (a) Find the Cartesian form of 2e2"/3. (b) Let the unit square S have vertices at the complex numbers 0, 1,1+ i,i. Find the images f(0), f(1), f(1+i), f(c) of the vertices of S, then sketch the unit square S and its image f(S) on the same set of axes. (c) Sketch the unit circle S1 and its image f(S!) on the same set of axes. (d) Show algebraically that, for any k, the curve Ck(t) = eik (2ein/3)' is an invariant curve of f. Use the GeoGebra link https://www.geogebra.org/m/w8gmjqha (also on Canvas) to investigate invariant curves and the transforma- tion f. =