Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((1+2i)\cdot (+6i)= +6 i+12i^2 = \color{red}{-12}\color{blue}{+6i}\)
2. \((3+3i)\cdot (-10i)= -30 i-30i^2 = \color{red}{30}\color{blue}{-30i}\)
3. \(\frac{-1+7i}{-1-2i}= \frac{-1+7i}{-1-2i} \cdot \frac{-1+2i}{-1+2i} = \frac{1-2i -7 i+14i^2 }{(-1)^2-(-2i)^2} = \frac{1-2i -7 i-14}{1 + 4} = \frac{-13-9i }{5} = \frac{-13}{5} + \frac{-9}{5}i \)
4. \((-4+4i) \cdot (5+10i)= -20-40i +20 i+40i^2 = -20-40i +20 i-40= \color{red}{-20-40}\color{blue}{-40i +20i}=\color{red}{-60}\color{blue}{-20i}\)
5. \(\frac{5+10i}{9+6i}= \frac{5+10i}{9+6i} \cdot \frac{9-6i}{9-6i} = \frac{45-30i +90 i-60i^2 }{(9)^2-(6i)^2} = \frac{45-30i +90 i+60}{81 + 36} = \frac{105+60i }{117} = \frac{35}{39} - \frac{-20}{39}i \)
6. \((-10i) \cdot (-9-5i)= +90 i+50i^2 = \color{red}{-50}\color{blue}{+90i}\)
7. \((-2-7i)-(7+2i)= -2-7i -7-2i =\color{red}{-2-7}\color{blue}{-7i -2i}=\color{red}{-9}\color{blue}{-9i}\)
8. \((8-7i)-(-2+4i)= 8-7i +2-4i =\color{red}{8+2}\color{blue}{-7i -4i}=\color{red}{10}\color{blue}{-11i}\)
9. \((9-7i) \cdot (7+7i)= 63+63i -49 i-49i^2 = 63+63i -49 i+49= \color{red}{63+49}\color{blue}{+63i -49i}=\color{red}{112}\color{blue}{+14i}\)
10. \((2-6i)-(4+3i)= 2-6i -4-3i =\color{red}{2-4}\color{blue}{-6i -3i}=\color{red}{-2}\color{blue}{-9i}\)
11. \((4-i)\cdot (-3i)= -12 i+3i^2 = \color{red}{-3}\color{blue}{-12i}\)
12. \((3-5i) \cdot (-3+5i)= -9+15i +15 i-25i^2 = -9+15i +15 i+25= \color{red}{-9+25}\color{blue}{+15i +15i}=\color{red}{16}\color{blue}{+30i}\)