Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3i) \cdot (-1+i)= +3 i-3i^2 = \color{red}{3}\color{blue}{+3i}\)
2. \((-6-9i)-(9-8i)= -6-9i -9+8i =\color{red}{-6-9}\color{blue}{-9i +8i}=\color{red}{-15}\color{blue}{-i}\)
3. \(\frac{9+i}{-2-9i}= \frac{9+i}{-2-9i} \cdot \frac{-2+9i}{-2+9i} = \frac{-18+81i -2 i+9i^2 }{(-2)^2-(-9i)^2} = \frac{-18+81i -2 i-9}{4 + 81} = \frac{-27+79i }{85} = \frac{-27}{85} - \frac{-79}{85}i \)
4. \(\frac{5-9i}{-1+7i}= \frac{5-9i}{-1+7i} \cdot \frac{-1-7i}{-1-7i} = \frac{-5-35i +9 i+63i^2 }{(-1)^2-(7i)^2} = \frac{-5-35i +9 i-63}{1 + 49} = \frac{-68-26i }{50} = \frac{-34}{25} + \frac{-13}{25}i \)
5. \((2-10i) \cdot (-4-10i)= -8-20i +40 i+100i^2 = -8-20i +40 i-100= \color{red}{-8-100}\color{blue}{-20i +40i}=\color{red}{-108}\color{blue}{+20i}\)
6. \((-9+5i) \cdot (-10+4i)= 90-36i -50 i+20i^2 = 90-36i -50 i-20= \color{red}{90-20}\color{blue}{-36i -50i}=\color{red}{70}\color{blue}{-86i}\)
7. \(\frac{-5+5i}{-7-10i}= \frac{-5+5i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{35-50i -35 i+50i^2 }{(-7)^2-(-10i)^2} = \frac{35-50i -35 i-50}{49 + 100} = \frac{-15-85i }{149} = \frac{-15}{149} + \frac{-85}{149}i \)
8. \((-5i) \cdot (-4-9i)= +20 i+45i^2 = \color{red}{-45}\color{blue}{+20i}\)
9. \((-4i) \cdot (-4-9i)= +16 i+36i^2 = \color{red}{-36}\color{blue}{+16i}\)
10. \((7-2i) \cdot (-1-4i)= -7-28i +2 i+8i^2 = -7-28i +2 i-8= \color{red}{-7-8}\color{blue}{-28i +2i}=\color{red}{-15}\color{blue}{-26i}\)
11. \((-8+5i)+(-2-3i)= -8+5i -2-3i =\color{red}{-8-2}\color{blue}{+5i -3i}=\color{red}{-10}\color{blue}{+2i}\)
12. \((-9-i)-(8-3i)= -9-i -8+3i =\color{red}{-9-8}\color{blue}{-i +3i}=\color{red}{-17}\color{blue}{+2i}\)