21 lines
482 B
Markdown
21 lines
482 B
Markdown
# 1.
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3)
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$z = ( 1 - i )^6 = [(1-i)^2]^3= (1^2 - 2i +i^2)^3 = (-2i)^3 = -8i^3 = -8\times-i= 8i$
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$\Re{z}=0$
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$\Im{z}=8$
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$\bar z = -8i$
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$|z| = \sqrt{0^2+8^2}= \sqrt{64} = 8$
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9)
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$z = \frac{20-5i}{(1-2i)(i+3)}=\frac{20-5i}{i+3-2i^2-6i}=\frac{20-5i}{5-5i} \times \frac{5+5i}{5+5i}=\frac{100+40i-25i+25}{50}=\frac{125+15i}{50}=\frac{25+3i}{10}=2.5+0.3i$
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$\Re = 2.5$
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$\Im=0.3$
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$\bar z = 2.5 + 0.3i$
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$|z|=\sqrt{2.5^2+0.3^2} = \sqrt{12.5+0.09} = 2.51793566240283$
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![[li_zesp.pdf]] |