Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-7i) \cdot (-10+3i)= 40-12i +70 i-21i^2 = 40-12i +70 i+21= \color{red}{40+21}\color{blue}{-12i +70i}=\color{red}{61}\color{blue}{+58i}\)
2. \((-10-i)\cdot (+10i)= -100 i-10i^2 = \color{red}{10}\color{blue}{-100i}\)
3. \(\frac{10-9i}{1+8i}= \frac{10-9i}{1+8i} \cdot \frac{1-8i}{1-8i} = \frac{10-80i -9 i+72i^2 }{(1)^2-(8i)^2} = \frac{10-80i -9 i-72}{1 + 64} = \frac{-62-89i }{65} = \frac{-62}{65} + \frac{-89}{65}i \)
4. \(\frac{2-i}{-3-4i}= \frac{2-i}{-3-4i} \cdot \frac{-3+4i}{-3+4i} = \frac{-6+8i +3 i-4i^2 }{(-3)^2-(-4i)^2} = \frac{-6+8i +3 i+4}{9 + 16} = \frac{-2+11i }{25} = \frac{-2}{25} - \frac{-11}{25}i \)
5. \(\frac{1+5i}{-2+3i}= \frac{1+5i}{-2+3i} \cdot \frac{-2-3i}{-2-3i} = \frac{-2-3i -10 i-15i^2 }{(-2)^2-(3i)^2} = \frac{-2-3i -10 i+15}{4 + 9} = \frac{13-13i }{13} = 1+ 1i\)
6. \((-6-5i) \cdot (5-i)= -30+6i -25 i+5i^2 = -30+6i -25 i-5= \color{red}{-30-5}\color{blue}{+6i -25i}=\color{red}{-35}\color{blue}{-19i}\)
7. \(\frac{10-5i}{3+7i}= \frac{10-5i}{3+7i} \cdot \frac{3-7i}{3-7i} = \frac{30-70i -15 i+35i^2 }{(3)^2-(7i)^2} = \frac{30-70i -15 i-35}{9 + 49} = \frac{-5-85i }{58} = \frac{-5}{58} + \frac{-85}{58}i \)
8. \((8+4i) \cdot (4-i)= 32-8i +16 i-4i^2 = 32-8i +16 i+4= \color{red}{32+4}\color{blue}{-8i +16i}=\color{red}{36}\color{blue}{+8i}\)
9. \((8-i) \cdot (-3-7i)= -24-56i +3 i+7i^2 = -24-56i +3 i-7= \color{red}{-24-7}\color{blue}{-56i +3i}=\color{red}{-31}\color{blue}{-53i}\)
10. \((-1+9i)\cdot (+9i)= -9 i+81i^2 = \color{red}{-81}\color{blue}{-9i}\)
11. \((3-9i) \cdot (8+i)= 24+3i -72 i-9i^2 = 24+3i -72 i+9= \color{red}{24+9}\color{blue}{+3i -72i}=\color{red}{33}\color{blue}{-69i}\)
12. \(\frac{6-4i}{-5+2i}= \frac{6-4i}{-5+2i} \cdot \frac{-5-2i}{-5-2i} = \frac{-30-12i +20 i+8i^2 }{(-5)^2-(2i)^2} = \frac{-30-12i +20 i-8}{25 + 4} = \frac{-38+8i }{29} = \frac{-38}{29} - \frac{-8}{29}i \)