Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-2i)\cdot (+i)= -1 i-2i^2 = \color{red}{2}\color{blue}{-i}\)
2. \((-8+2i)\cdot (-i)= +8 i-2i^2 = \color{red}{2}\color{blue}{+8i}\)
3. \((-5-8i) \cdot (-8+9i)= 40-45i +64 i-72i^2 = 40-45i +64 i+72= \color{red}{40+72}\color{blue}{-45i +64i}=\color{red}{112}\color{blue}{+19i}\)
4. \((9-4i) \cdot (9+2i)= 81+18i -36 i-8i^2 = 81+18i -36 i+8= \color{red}{81+8}\color{blue}{+18i -36i}=\color{red}{89}\color{blue}{-18i}\)
5. \((1-6i) \cdot (1-2i)= 1-2i -6 i+12i^2 = 1-2i -6 i-12= \color{red}{1-12}\color{blue}{-2i -6i}=\color{red}{-11}\color{blue}{-8i}\)
6. \((7+i) \cdot (4+i)= 28+7i +4 i+i^2 = 28+7i +4 i-= \color{red}{28-1}\color{blue}{+7i +4i}=\color{red}{27}\color{blue}{+11i}\)
7. \((+10i) \cdot (1+4i)= +10 i+40i^2 = \color{red}{-40}\color{blue}{+10i}\)
8. \(\frac{-2-7i}{10+8i}= \frac{-2-7i}{10+8i} \cdot \frac{10-8i}{10-8i} = \frac{-20+16i -70 i+56i^2 }{(10)^2-(8i)^2} = \frac{-20+16i -70 i-56}{100 + 64} = \frac{-76-54i }{164} = \frac{-19}{41} + \frac{-27}{82}i \)
9. \(\frac{5+i}{4+3i}= \frac{5+i}{4+3i} \cdot \frac{4-3i}{4-3i} = \frac{20-15i +4 i-3i^2 }{(4)^2-(3i)^2} = \frac{20-15i +4 i+3}{16 + 9} = \frac{23-11i }{25} = \frac{23}{25} + \frac{-11}{25}i \)
10. \((4-10i) \cdot (-1-2i)= -4-8i +10 i+20i^2 = -4-8i +10 i-20= \color{red}{-4-20}\color{blue}{-8i +10i}=\color{red}{-24}\color{blue}{+2i}\)
11. \((9+4i) \cdot (2-5i)= 18-45i +8 i-20i^2 = 18-45i +8 i+20= \color{red}{18+20}\color{blue}{-45i +8i}=\color{red}{38}\color{blue}{-37i}\)
12. \((+3i) \cdot (-6-i)= -18 i-3i^2 = \color{red}{3}\color{blue}{-18i}\)