Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((3+9i) \cdot (9-8i)= 27-24i +81 i-72i^2 = 27-24i +81 i+72= \color{red}{27+72}\color{blue}{-24i +81i}=\color{red}{99}\color{blue}{+57i}\)
2. \((-8i) \cdot (3+8i)= -24 i-64i^2 = \color{red}{64}\color{blue}{-24i}\)
3. \((9+9i)\cdot (-6i)= -54 i-54i^2 = \color{red}{54}\color{blue}{-54i}\)
4. \((7+5i)\cdot (+10i)= +70 i+50i^2 = \color{red}{-50}\color{blue}{+70i}\)
5. \((5-i) \cdot (-9-2i)= -45-10i +9 i+2i^2 = -45-10i +9 i-2= \color{red}{-45-2}\color{blue}{-10i +9i}=\color{red}{-47}\color{blue}{-i}\)
6. \((-1+2i)\cdot (-9i)= +9 i-18i^2 = \color{red}{18}\color{blue}{+9i}\)
7. \((+6i) \cdot (9+9i)= +54 i+54i^2 = \color{red}{-54}\color{blue}{+54i}\)
8. \(\frac{-10+2i}{-1-5i}= \frac{-10+2i}{-1-5i} \cdot \frac{-1+5i}{-1+5i} = \frac{10-50i -2 i+10i^2 }{(-1)^2-(-5i)^2} = \frac{10-50i -2 i-10}{1 + 25} = \frac{0-52i }{26} = 0+ 2i\)
9. \((8+5i)\cdot (-7i)= -56 i-35i^2 = \color{red}{35}\color{blue}{-56i}\)
10. \((-1+5i) \cdot (-2+2i)= 2-2i -10 i+10i^2 = 2-2i -10 i-10= \color{red}{2-10}\color{blue}{-2i -10i}=\color{red}{-8}\color{blue}{-12i}\)
11. \((-i) \cdot (-3+6i)= +3 i-6i^2 = \color{red}{6}\color{blue}{+3i}\)
12. \((3+i) \cdot (1-5i)= 3-15i +1 i-5i^2 = 3-15i +1 i+5= \color{red}{3+5}\color{blue}{-15i +i}=\color{red}{8}\color{blue}{-14i}\)