Basisbewerkingen gemengd (a+bi)

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Bereken

1. \((10+10i)+(7-9i)\)
2. \((5-3i)+(10+4i)\)
3. \((-2-8i) \cdot (-10-7i)\)
4. \((7+8i) \cdot (5-8i)\)
5. \(\frac{-10-2i}{3-3i}\)
6. \(\frac{-9+6i}{-3+2i}\)
7. \((-9-10i)\cdot (-3i)\)
8. \((-9+10i) \cdot (-2-7i)\)
9. \((6-9i) \cdot (-6+6i)\)
10. \((4+10i)\cdot (-10i)\)
11. \(\frac{-4-4i}{-9+i}\)
12. \(\frac{5+i}{-3+7i}\)

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Bereken

Verbetersleutel

1. \((10+10i)+(7-9i)= 10+10i +7-9i =\color{red}{10+7}\color{blue}{+10i -9i}=\color{red}{17}\color{blue}{+i}\)
2. \((5-3i)+(10+4i)= 5-3i +10+4i =\color{red}{5+10}\color{blue}{-3i +4i}=\color{red}{15}\color{blue}{+i}\)
3. \((-2-8i) \cdot (-10-7i)= 20+14i +80 i+56i^2 = 20+14i +80 i-56= \color{red}{20-56}\color{blue}{+14i +80i}=\color{red}{-36}\color{blue}{+94i}\)
4. \((7+8i) \cdot (5-8i)= 35-56i +40 i-64i^2 = 35-56i +40 i+64= \color{red}{35+64}\color{blue}{-56i +40i}=\color{red}{99}\color{blue}{-16i}\)
5. \(\frac{-10-2i}{3-3i}= \frac{-10-2i}{3-3i} \cdot \frac{3+3i}{3+3i} = \frac{-30-30i -6 i-6i^2 }{(3)^2-(-3i)^2} = \frac{-30-30i -6 i+6}{9 + 9} = \frac{-24-36i }{18} = \frac{-4}{3} + 2i\)
6. \(\frac{-9+6i}{-3+2i}= \frac{-9+6i}{-3+2i} \cdot \frac{-3-2i}{-3-2i} = \frac{27+18i -18 i-12i^2 }{(-3)^2-(2i)^2} = \frac{27+18i -18 i+12}{9 + 4} = \frac{39+0i }{13} = 3+ 0i\)
7. \((-9-10i)\cdot (-3i)= +27 i+30i^2 = \color{red}{-30}\color{blue}{+27i}\)
8. \((-9+10i) \cdot (-2-7i)= 18+63i -20 i-70i^2 = 18+63i -20 i+70= \color{red}{18+70}\color{blue}{+63i -20i}=\color{red}{88}\color{blue}{+43i}\)
9. \((6-9i) \cdot (-6+6i)= -36+36i +54 i-54i^2 = -36+36i +54 i+54= \color{red}{-36+54}\color{blue}{+36i +54i}=\color{red}{18}\color{blue}{+90i}\)
10. \((4+10i)\cdot (-10i)= -40 i-100i^2 = \color{red}{100}\color{blue}{-40i}\)
11. \(\frac{-4-4i}{-9+i}= \frac{-4-4i}{-9+i} \cdot \frac{-9-i}{-9-i} = \frac{36+4i +36 i+4i^2 }{(-9)^2-(1i)^2} = \frac{36+4i +36 i-4}{81 + 1} = \frac{32+40i }{82} = \frac{16}{41} - \frac{-20}{41}i \)
12. \(\frac{5+i}{-3+7i}= \frac{5+i}{-3+7i} \cdot \frac{-3-7i}{-3-7i} = \frac{-15-35i -3 i-7i^2 }{(-3)^2-(7i)^2} = \frac{-15-35i -3 i+7}{9 + 49} = \frac{-8-38i }{58} = \frac{-4}{29} + \frac{-19}{29}i \)