Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-5i) \cdot (-9-9i)= 9+9i +45 i+45i^2 = 9+9i +45 i-45= \color{red}{9-45}\color{blue}{+9i +45i}=\color{red}{-36}\color{blue}{+54i}\)
2. \((4-2i)-(-4-4i)= 4-2i +4+4i =\color{red}{4+4}\color{blue}{-2i +4i}=\color{red}{8}\color{blue}{+2i}\)
3. \((-1-5i)+(10+4i)= -1-5i +10+4i =\color{red}{-1+10}\color{blue}{-5i +4i}=\color{red}{9}\color{blue}{-i}\)
4. \((3+3i) \cdot (5+10i)= 15+30i +15 i+30i^2 = 15+30i +15 i-30= \color{red}{15-30}\color{blue}{+30i +15i}=\color{red}{-15}\color{blue}{+45i}\)
5. \(\frac{-1+10i}{-1-7i}= \frac{-1+10i}{-1-7i} \cdot \frac{-1+7i}{-1+7i} = \frac{1-7i -10 i+70i^2 }{(-1)^2-(-7i)^2} = \frac{1-7i -10 i-70}{1 + 49} = \frac{-69-17i }{50} = \frac{-69}{50} + \frac{-17}{50}i \)
6. \((-9i) \cdot (-5-i)= +45 i+9i^2 = \color{red}{-9}\color{blue}{+45i}\)
7. \((-8+8i) \cdot (-3+8i)= 24-64i -24 i+64i^2 = 24-64i -24 i-64= \color{red}{24-64}\color{blue}{-64i -24i}=\color{red}{-40}\color{blue}{-88i}\)
8. \((1+6i)+(2+2i)= 1+6i +2+2i =\color{red}{1+2}\color{blue}{+6i +2i}=\color{red}{3}\color{blue}{+8i}\)
9. \((2-10i)-(-3-7i)= 2-10i +3+7i =\color{red}{2+3}\color{blue}{-10i +7i}=\color{red}{5}\color{blue}{-3i}\)
10. \(\frac{5+6i}{-7+8i}= \frac{5+6i}{-7+8i} \cdot \frac{-7-8i}{-7-8i} = \frac{-35-40i -42 i-48i^2 }{(-7)^2-(8i)^2} = \frac{-35-40i -42 i+48}{49 + 64} = \frac{13-82i }{113} = \frac{13}{113} + \frac{-82}{113}i \)
11. \(\frac{-1+6i}{3+10i}= \frac{-1+6i}{3+10i} \cdot \frac{3-10i}{3-10i} = \frac{-3+10i +18 i-60i^2 }{(3)^2-(10i)^2} = \frac{-3+10i +18 i+60}{9 + 100} = \frac{57+28i }{109} = \frac{57}{109} - \frac{-28}{109}i \)
12. \((9-7i)-(6+6i)= 9-7i -6-6i =\color{red}{9-6}\color{blue}{-7i -6i}=\color{red}{3}\color{blue}{-13i}\)