# 1.

3)

$z = ( 1 - i )^6 = [(1-i)^2]^3= (1^2 - 2i +i^2)^3 = (-2i)^3 = -8i^3 = -8\times-i= 8i$

$\Re{z}=0$
$\Im{z}=8$

$\bar z = -8i$

$|z| = \sqrt{0^2+8^2}= \sqrt{64} = 8$

  
9)  
$z = \frac{20-5i}{(1-2i)(i+3)}=\frac{20-5i}{i+3-2i^2-6i}=\frac{20-5i}{5-5i} \times \frac{5+5i}{5+5i}=\frac{100+40i-25i+25}{50}=\frac{125+15i}{50}=\frac{25+3i}{10}=2.5+0.3i$
$\Re = 2.5$
$\Im=0.3$ 
$\bar z = 2.5 + 0.3i$  
$|z|=\sqrt{2.5^2+0.3^2} = \sqrt{12.5+0.09} = 2.51793566240283$
![[li_zesp.pdf]]