[tex]a)z= \frac{1}{3-2i} = \frac{3+2i}{13} ;Rez= \frac{3}{13};Imz= \frac{2i}{13} \\ b)z= \frac{1-4i}{1+5i} = \frac{(1-4i)(1-5i)}{(1+5i)(1+4i)}= \frac{-19-9i}{-19+9i}= \frac{-(19+9i)(19+9i)}{-(19-9i)(19+9i)}= \\ = \frac{361+342i-81}{361+81} = \frac{280+342i}{442};Rez= \frac{280}{442};Imz= \frac{342i}{442} \\ c)z= (\frac{1-i}{1+i})^2= \frac{1-2i-1}{1+2i-1}}= -1 ;Rez=-1;Imz=0[/tex]
