Răspuns:
Explicație pas cu pas:
a) (1-i)/(2+i) = (1-i)(2-i)/[(2+i)(2-i)] = (2-i-2i+i²)/(4-i²) =
= (2-3i-1)/(4+1) = (1-3i)/5
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b) 10/(3-i) = (3+i)/[(3-i)(3+i)] = (3+i)/(9+1) = (3+i)/10
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c) 29/(5-2i)-25/(4-3i) = 29(5+2i)/[(5-2i)(5+2i)]-25(4+3i)/[(4-3i)(4+3i)]=
= 29(5+2i)/29 - 25(4+3i)/25 = 5+2i-4-3i = 1-i
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d) (5-i)/3i+2i = (5-i)·i/(-3) + 2i = (5i+1-6i)/(-3) = (i-1)/3
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e) (7-3i)/(3+2i) = (7-3i)(3-2i)/[(3+2i)(3-2i)] = (21-14i-9i+6i²)/(9-4i²) =
= (15-23i)/13
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f) (4+3i)/(4-3i) + (5-4i)/(4+3i) = [(4+3i)²+(5-4i)(4-3i)]/[(4-3i)(4+3i)] =
= (16+24i-9+20-15i-16i-12)/(16+9) = (15-7i)/25
