Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5-3i)\cdot (+6i)= +30 i-18i^2 = \color{red}{18}\color{blue}{+30i}\)
2. \(\frac{4-5i}{-9+6i}= \frac{4-5i}{-9+6i} \cdot \frac{-9-6i}{-9-6i} = \frac{-36-24i +45 i+30i^2 }{(-9)^2-(6i)^2} = \frac{-36-24i +45 i-30}{81 + 36} = \frac{-66+21i }{117} = \frac{-22}{39} - \frac{-7}{39}i \)
3. \((7-4i) \cdot (9-7i)= 63-49i -36 i+28i^2 = 63-49i -36 i-28= \color{red}{63-28}\color{blue}{-49i -36i}=\color{red}{35}\color{blue}{-85i}\)
4. \(\frac{2-10i}{9-8i}= \frac{2-10i}{9-8i} \cdot \frac{9+8i}{9+8i} = \frac{18+16i -90 i-80i^2 }{(9)^2-(-8i)^2} = \frac{18+16i -90 i+80}{81 + 64} = \frac{98-74i }{145} = \frac{98}{145} + \frac{-74}{145}i \)
5. \((-7+8i) \cdot (4-4i)= -28+28i +32 i-32i^2 = -28+28i +32 i+32= \color{red}{-28+32}\color{blue}{+28i +32i}=\color{red}{4}\color{blue}{+60i}\)
6. \((4+i) \cdot (10+8i)= 40+32i +10 i+8i^2 = 40+32i +10 i-8= \color{red}{40-8}\color{blue}{+32i +10i}=\color{red}{32}\color{blue}{+42i}\)
7. \((6+7i)\cdot (+i)= +6 i+7i^2 = \color{red}{-7}\color{blue}{+6i}\)
8. \((6-7i)\cdot (-2i)= -12 i+14i^2 = \color{red}{-14}\color{blue}{-12i}\)
9. \((1-2i)\cdot (+5i)= +5 i-10i^2 = \color{red}{10}\color{blue}{+5i}\)
10. \((-2i) \cdot (3+8i)= -6 i-16i^2 = \color{red}{16}\color{blue}{-6i}\)
11. \((-7+8i) \cdot (8-7i)= -56+49i +64 i-56i^2 = -56+49i +64 i+56= \color{red}{-56+56}\color{blue}{+49i +64i}=\color{blue}{113i}\)
12. \((2+10i) \cdot (-9+6i)= -18+12i -90 i+60i^2 = -18+12i -90 i-60= \color{red}{-18-60}\color{blue}{+12i -90i}=\color{red}{-78}\color{blue}{-78i}\)