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Polsl-Notes/AMiAL/ICT/Ćwiczenia/1 SEM/20221014121234.md

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1.

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

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