Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-5i)-(-6+i)= 7-5i +6-i =\color{red}{7+6}\color{blue}{-5i -i}=\color{red}{13}\color{blue}{-6i}\)
2. \((6+7i)-(-3-10i)= 6+7i +3+10i =\color{red}{6+3}\color{blue}{+7i +10i}=\color{red}{9}\color{blue}{+17i}\)
3. \((9-10i)+(4-2i)= 9-10i +4-2i =\color{red}{9+4}\color{blue}{-10i -2i}=\color{red}{13}\color{blue}{-12i}\)
4. \((3+4i)-(-8+3i)= 3+4i +8-3i =\color{red}{3+8}\color{blue}{+4i -3i}=\color{red}{11}\color{blue}{+i}\)
5. \((2-9i)-(1+7i)= 2-9i -1-7i =\color{red}{2-1}\color{blue}{-9i -7i}=\color{red}{1}\color{blue}{-16i}\)
6. \((-9-10i)\cdot (-10i)= +90 i+100i^2 = \color{red}{-100}\color{blue}{+90i}\)
7. \((-7+5i)-(-7-5i)= -7+5i +7+5i =\color{red}{-7+7}\color{blue}{+5i +5i}=\color{blue}{10i}\)
8. \((-9+4i)-(9-10i)= -9+4i -9+10i =\color{red}{-9-9}\color{blue}{+4i +10i}=\color{red}{-18}\color{blue}{+14i}\)
9. \((2-2i) \cdot (-2-i)= -4-2i +4 i+2i^2 = -4-2i +4 i-2= \color{red}{-4-2}\color{blue}{-2i +4i}=\color{red}{-6}\color{blue}{+2i}\)
10. \(\frac{3-3i}{-4+5i}= \frac{3-3i}{-4+5i} \cdot \frac{-4-5i}{-4-5i} = \frac{-12-15i +12 i+15i^2 }{(-4)^2-(5i)^2} = \frac{-12-15i +12 i-15}{16 + 25} = \frac{-27-3i }{41} = \frac{-27}{41} + \frac{-3}{41}i \)
11. \((-8+3i)+(-8+5i)= -8+3i -8+5i =\color{red}{-8-8}\color{blue}{+3i +5i}=\color{red}{-16}\color{blue}{+8i}\)
12. \((-5-8i) \cdot (8-4i)= -40+20i -64 i+32i^2 = -40+20i -64 i-32= \color{red}{-40-32}\color{blue}{+20i -64i}=\color{red}{-72}\color{blue}{-44i}\)