Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9+10i) \cdot (-10+5i)= 90-45i -100 i+50i^2 = 90-45i -100 i-50= \color{red}{90-50}\color{blue}{-45i -100i}=\color{red}{40}\color{blue}{-145i}\)
2. \((7-9i)-(6-8i)= 7-9i -6+8i =\color{red}{7-6}\color{blue}{-9i +8i}=\color{red}{1}\color{blue}{-i}\)
3. \(\frac{9-4i}{-8+4i}= \frac{9-4i}{-8+4i} \cdot \frac{-8-4i}{-8-4i} = \frac{-72-36i +32 i+16i^2 }{(-8)^2-(4i)^2} = \frac{-72-36i +32 i-16}{64 + 16} = \frac{-88-4i }{80} = \frac{-11}{10} + \frac{-1}{20}i \)
4. \((-6-9i)+(3+9i)= -6-9i +3+9i =\color{red}{-6+3}\color{blue}{-9i +9i}=\color{red}{-3}\)
5. \((4-3i)\cdot (+3i)= +12 i-9i^2 = \color{red}{9}\color{blue}{+12i}\)
6. \((3-9i)-(-8+10i)= 3-9i +8-10i =\color{red}{3+8}\color{blue}{-9i -10i}=\color{red}{11}\color{blue}{-19i}\)
7. \((-3i) \cdot (-1-3i)= +3 i+9i^2 = \color{red}{-9}\color{blue}{+3i}\)
8. \((-9i) \cdot (-9+9i)= +81 i-81i^2 = \color{red}{81}\color{blue}{+81i}\)
9. \((-2-9i)-(2-7i)= -2-9i -2+7i =\color{red}{-2-2}\color{blue}{-9i +7i}=\color{red}{-4}\color{blue}{-2i}\)
10. \((-5+8i) \cdot (9+7i)= -45-35i +72 i+56i^2 = -45-35i +72 i-56= \color{red}{-45-56}\color{blue}{-35i +72i}=\color{red}{-101}\color{blue}{+37i}\)
11. \(\frac{-7-2i}{10-i}= \frac{-7-2i}{10-i} \cdot \frac{10+i}{10+i} = \frac{-70-7i -20 i-2i^2 }{(10)^2-(-1i)^2} = \frac{-70-7i -20 i+2}{100 + 1} = \frac{-68-27i }{101} = \frac{-68}{101} + \frac{-27}{101}i \)
12. \((4-3i)+(3-5i)= 4-3i +3-5i =\color{red}{4+3}\color{blue}{-3i -5i}=\color{red}{7}\color{blue}{-8i}\)