Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((4-4i)-(-1+i)= 4-4i +1-i =\color{red}{4+1}\color{blue}{-4i -i}=\color{red}{5}\color{blue}{-5i}\)
2. \((-4+9i)-(-7-3i)= -4+9i +7+3i =\color{red}{-4+7}\color{blue}{+9i +3i}=\color{red}{3}\color{blue}{+12i}\)
3. \((5-8i)-(3+10i)= 5-8i -3-10i =\color{red}{5-3}\color{blue}{-8i -10i}=\color{red}{2}\color{blue}{-18i}\)
4. \((-7-3i)+(7+2i)= -7-3i +7+2i =\color{red}{-7+7}\color{blue}{-3i +2i}=\color{blue}{-i}\)
5. \((10+4i) \cdot (-3+9i)= -30+90i -12 i+36i^2 = -30+90i -12 i-36= \color{red}{-30-36}\color{blue}{+90i -12i}=\color{red}{-66}\color{blue}{+78i}\)
6. \(\frac{9-4i}{-1+i}= \frac{9-4i}{-1+i} \cdot \frac{-1-i}{-1-i} = \frac{-9-9i +4 i+4i^2 }{(-1)^2-(1i)^2} = \frac{-9-9i +4 i-4}{1 + 1} = \frac{-13-5i }{2} = \frac{-13}{2} + \frac{-5}{2}i \)
7. \((+10i) \cdot (-9+i)= -90 i+10i^2 = \color{red}{-10}\color{blue}{-90i}\)
8. \(\frac{5-9i}{7-4i}= \frac{5-9i}{7-4i} \cdot \frac{7+4i}{7+4i} = \frac{35+20i -63 i-36i^2 }{(7)^2-(-4i)^2} = \frac{35+20i -63 i+36}{49 + 16} = \frac{71-43i }{65} = \frac{71}{65} + \frac{-43}{65}i \)
9. \((7+3i) \cdot (-6-2i)= -42-14i -18 i-6i^2 = -42-14i -18 i+6= \color{red}{-42+6}\color{blue}{-14i -18i}=\color{red}{-36}\color{blue}{-32i}\)
10. \((1-2i) \cdot (4-6i)= 4-6i -8 i+12i^2 = 4-6i -8 i-12= \color{red}{4-12}\color{blue}{-6i -8i}=\color{red}{-8}\color{blue}{-14i}\)
11. \((1-4i) \cdot (2+i)= 2+i -8 i-4i^2 = 2+i -8 i+4= \color{red}{2+4}\color{blue}{+i -8i}=\color{red}{6}\color{blue}{-7i}\)
12. \((4+10i) \cdot (-1-7i)= -4-28i -10 i-70i^2 = -4-28i -10 i+70= \color{red}{-4+70}\color{blue}{-28i -10i}=\color{red}{66}\color{blue}{-38i}\)