Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7+9i) \cdot (-3+3i)= -21+21i -27 i+27i^2 = -21+21i -27 i-27= \color{red}{-21-27}\color{blue}{+21i -27i}=\color{red}{-48}\color{blue}{-6i}\)
2. \((5+i)+(-4+3i)= 5+i -4+3i =\color{red}{5-4}\color{blue}{+i +3i}=\color{red}{1}\color{blue}{+4i}\)
3. \(\frac{1-4i}{7+3i}= \frac{1-4i}{7+3i} \cdot \frac{7-3i}{7-3i} = \frac{7-3i -28 i+12i^2 }{(7)^2-(3i)^2} = \frac{7-3i -28 i-12}{49 + 9} = \frac{-5-31i }{58} = \frac{-5}{58} + \frac{-31}{58}i \)
4. \((-1+8i)\cdot (+8i)= -8 i+64i^2 = \color{red}{-64}\color{blue}{-8i}\)
5. \((6+3i)+(7+2i)= 6+3i +7+2i =\color{red}{6+7}\color{blue}{+3i +2i}=\color{red}{13}\color{blue}{+5i}\)
6. \((6+5i) \cdot (-8+3i)= -48+18i -40 i+15i^2 = -48+18i -40 i-15= \color{red}{-48-15}\color{blue}{+18i -40i}=\color{red}{-63}\color{blue}{-22i}\)
7. \(\frac{-8-10i}{3+10i}= \frac{-8-10i}{3+10i} \cdot \frac{3-10i}{3-10i} = \frac{-24+80i -30 i+100i^2 }{(3)^2-(10i)^2} = \frac{-24+80i -30 i-100}{9 + 100} = \frac{-124+50i }{109} = \frac{-124}{109} - \frac{-50}{109}i \)
8. \((-4-6i)\cdot (-8i)= +32 i+48i^2 = \color{red}{-48}\color{blue}{+32i}\)
9. \((10+3i)\cdot (-3i)= -30 i-9i^2 = \color{red}{9}\color{blue}{-30i}\)
10. \(\frac{1+9i}{-2+8i}= \frac{1+9i}{-2+8i} \cdot \frac{-2-8i}{-2-8i} = \frac{-2-8i -18 i-72i^2 }{(-2)^2-(8i)^2} = \frac{-2-8i -18 i+72}{4 + 64} = \frac{70-26i }{68} = \frac{35}{34} + \frac{-13}{34}i \)
11. \(\frac{-3-7i}{9-3i}= \frac{-3-7i}{9-3i} \cdot \frac{9+3i}{9+3i} = \frac{-27-9i -63 i-21i^2 }{(9)^2-(-3i)^2} = \frac{-27-9i -63 i+21}{81 + 9} = \frac{-6-72i }{90} = \frac{-1}{15} + \frac{-4}{5}i \)
12. \((-10+2i)+(8-2i)= -10+2i +8-2i =\color{red}{-10+8}\color{blue}{+2i -2i}=\color{red}{-2}\)