Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9i) \cdot (7-9i)= -63 i+81i^2 = \color{red}{-81}\color{blue}{-63i}\)
2. \(\frac{-8+6i}{3-i}= \frac{-8+6i}{3-i} \cdot \frac{3+i}{3+i} = \frac{-24-8i +18 i+6i^2 }{(3)^2-(-1i)^2} = \frac{-24-8i +18 i-6}{9 + 1} = \frac{-30+10i }{10} = -3- -1i\)
3. \((-3i) \cdot (-7+4i)= +21 i-12i^2 = \color{red}{12}\color{blue}{+21i}\)
4. \((-5+9i) \cdot (-8+3i)= 40-15i -72 i+27i^2 = 40-15i -72 i-27= \color{red}{40-27}\color{blue}{-15i -72i}=\color{red}{13}\color{blue}{-87i}\)
5. \(\frac{-8+7i}{-7+8i}= \frac{-8+7i}{-7+8i} \cdot \frac{-7-8i}{-7-8i} = \frac{56+64i -49 i-56i^2 }{(-7)^2-(8i)^2} = \frac{56+64i -49 i+56}{49 + 64} = \frac{112+15i }{113} = \frac{112}{113} - \frac{-15}{113}i \)
6. \((+4i) \cdot (-10-9i)= -40 i-36i^2 = \color{red}{36}\color{blue}{-40i}\)
7. \((+10i) \cdot (1-8i)= +10 i-80i^2 = \color{red}{80}\color{blue}{+10i}\)
8. \((-6+7i)\cdot (-5i)= +30 i-35i^2 = \color{red}{35}\color{blue}{+30i}\)
9. \(\frac{7+9i}{6-3i}= \frac{7+9i}{6-3i} \cdot \frac{6+3i}{6+3i} = \frac{42+21i +54 i+27i^2 }{(6)^2-(-3i)^2} = \frac{42+21i +54 i-27}{36 + 9} = \frac{15+75i }{45} = \frac{1}{3} - \frac{-5}{3}i \)
10. \((7-4i) \cdot (-10+2i)= -70+14i +40 i-8i^2 = -70+14i +40 i+8= \color{red}{-70+8}\color{blue}{+14i +40i}=\color{red}{-62}\color{blue}{+54i}\)
11. \((-10+7i) \cdot (-4-4i)= 40+40i -28 i-28i^2 = 40+40i -28 i+28= \color{red}{40+28}\color{blue}{+40i -28i}=\color{red}{68}\color{blue}{+12i}\)
12. \((-4-7i) \cdot (5-10i)= -20+40i -35 i+70i^2 = -20+40i -35 i-70= \color{red}{-20-70}\color{blue}{+40i -35i}=\color{red}{-90}\color{blue}{+5i}\)