Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5+i)+(-8+i)= -5+i -8+i =\color{red}{-5-8}\color{blue}{+i +i}=\color{red}{-13}\color{blue}{+2i}\)
2. \((-5+8i) \cdot (8+9i)= -40-45i +64 i+72i^2 = -40-45i +64 i-72= \color{red}{-40-72}\color{blue}{-45i +64i}=\color{red}{-112}\color{blue}{+19i}\)
3. \((-8i) \cdot (-4-2i)= +32 i+16i^2 = \color{red}{-16}\color{blue}{+32i}\)
4. \((-10+8i)-(3-9i)= -10+8i -3+9i =\color{red}{-10-3}\color{blue}{+8i +9i}=\color{red}{-13}\color{blue}{+17i}\)
5. \((-2+7i)-(6+10i)= -2+7i -6-10i =\color{red}{-2-6}\color{blue}{+7i -10i}=\color{red}{-8}\color{blue}{-3i}\)
6. \((6+5i)+(-10+8i)= 6+5i -10+8i =\color{red}{6-10}\color{blue}{+5i +8i}=\color{red}{-4}\color{blue}{+13i}\)
7. \((-5-8i)-(-4+7i)= -5-8i +4-7i =\color{red}{-5+4}\color{blue}{-8i -7i}=\color{red}{-1}\color{blue}{-15i}\)
8. \((10-3i)-(-9-2i)= 10-3i +9+2i =\color{red}{10+9}\color{blue}{-3i +2i}=\color{red}{19}\color{blue}{-i}\)
9. \(\frac{-9+2i}{3-7i}= \frac{-9+2i}{3-7i} \cdot \frac{3+7i}{3+7i} = \frac{-27-63i +6 i+14i^2 }{(3)^2-(-7i)^2} = \frac{-27-63i +6 i-14}{9 + 49} = \frac{-41-57i }{58} = \frac{-41}{58} + \frac{-57}{58}i \)
10. \((-6+10i)+(9-7i)= -6+10i +9-7i =\color{red}{-6+9}\color{blue}{+10i -7i}=\color{red}{3}\color{blue}{+3i}\)
11. \(\frac{-4-3i}{4+2i}= \frac{-4-3i}{4+2i} \cdot \frac{4-2i}{4-2i} = \frac{-16+8i -12 i+6i^2 }{(4)^2-(2i)^2} = \frac{-16+8i -12 i-6}{16 + 4} = \frac{-22-4i }{20} = \frac{-11}{10} + \frac{-1}{5}i \)
12. \((10-3i)+(-6-5i)= 10-3i -6-5i =\color{red}{10-6}\color{blue}{-3i -5i}=\color{red}{4}\color{blue}{-8i}\)