Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+4i)\cdot (-i)= +6 i-4i^2 = \color{red}{4}\color{blue}{+6i}\)
2. \(\frac{-10+10i}{4+5i}= \frac{-10+10i}{4+5i} \cdot \frac{4-5i}{4-5i} = \frac{-40+50i +40 i-50i^2 }{(4)^2-(5i)^2} = \frac{-40+50i +40 i+50}{16 + 25} = \frac{10+90i }{41} = \frac{10}{41} - \frac{-90}{41}i \)
3. \((-10+9i)+(1-5i)= -10+9i +1-5i =\color{red}{-10+1}\color{blue}{+9i -5i}=\color{red}{-9}\color{blue}{+4i}\)
4. \((-9+3i) \cdot (4+8i)= -36-72i +12 i+24i^2 = -36-72i +12 i-24= \color{red}{-36-24}\color{blue}{-72i +12i}=\color{red}{-60}\color{blue}{-60i}\)
5. \((-6+i) \cdot (-6-3i)= 36+18i -6 i-3i^2 = 36+18i -6 i+3= \color{red}{36+3}\color{blue}{+18i -6i}=\color{red}{39}\color{blue}{+12i}\)
6. \((9-3i) \cdot (-1-4i)= -9-36i +3 i+12i^2 = -9-36i +3 i-12= \color{red}{-9-12}\color{blue}{-36i +3i}=\color{red}{-21}\color{blue}{-33i}\)
7. \((-4-i)+(-10+10i)= -4-i -10+10i =\color{red}{-4-10}\color{blue}{-i +10i}=\color{red}{-14}\color{blue}{+9i}\)
8. \((10+9i)+(-4+6i)= 10+9i -4+6i =\color{red}{10-4}\color{blue}{+9i +6i}=\color{red}{6}\color{blue}{+15i}\)
9. \((1-i)-(-3-3i)= 1-i +3+3i =\color{red}{1+3}\color{blue}{-i +3i}=\color{red}{4}\color{blue}{+2i}\)
10. \((5+8i)+(2+i)= 5+8i +2+i =\color{red}{5+2}\color{blue}{+8i +i}=\color{red}{7}\color{blue}{+9i}\)
11. \(\frac{-3+3i}{-10-7i}= \frac{-3+3i}{-10-7i} \cdot \frac{-10+7i}{-10+7i} = \frac{30-21i -30 i+21i^2 }{(-10)^2-(-7i)^2} = \frac{30-21i -30 i-21}{100 + 49} = \frac{9-51i }{149} = \frac{9}{149} + \frac{-51}{149}i \)
12. \((1-8i) \cdot (-2-6i)= -2-6i +16 i+48i^2 = -2-6i +16 i-48= \color{red}{-2-48}\color{blue}{-6i +16i}=\color{red}{-50}\color{blue}{+10i}\)