Show z^2 maps the circle |z-1|=1 to a cardioid

  • Thread starter oab729
  • Start date
  • #1
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Homework Statement


show z^2 maps the circle |z-1|=1 to a cardioid 2(1+cos(theta))e^(i*theta)


Homework Equations





The Attempt at a Solution


I tried using the restriction |z-1| = 1 and simply got that r^2=2x.

Then I tried to apply that and got

z^2=2xe^(2i*theta)

I've been trying for a good 15 minutes.
 

Answers and Replies

  • #2
12
0
NVM, take z = 1+cos +isin
 

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