Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3+7i) \cdot (-4+9i)= 12-27i -28 i+63i^2 = 12-27i -28 i-63= \color{red}{12-63}\color{blue}{-27i -28i}=\color{red}{-51}\color{blue}{-55i}\)
2. \(\frac{-1+8i}{-5-i}= \frac{-1+8i}{-5-i} \cdot \frac{-5+i}{-5+i} = \frac{5-i -40 i+8i^2 }{(-5)^2-(-1i)^2} = \frac{5-i -40 i-8}{25 + 1} = \frac{-3-41i }{26} = \frac{-3}{26} + \frac{-41}{26}i \)
3. \((-10-6i)\cdot (-8i)= +80 i+48i^2 = \color{red}{-48}\color{blue}{+80i}\)
4. \((-7+3i) \cdot (-5+5i)= 35-35i -15 i+15i^2 = 35-35i -15 i-15= \color{red}{35-15}\color{blue}{-35i -15i}=\color{red}{20}\color{blue}{-50i}\)
5. \(\frac{7-9i}{-5+7i}= \frac{7-9i}{-5+7i} \cdot \frac{-5-7i}{-5-7i} = \frac{-35-49i +45 i+63i^2 }{(-5)^2-(7i)^2} = \frac{-35-49i +45 i-63}{25 + 49} = \frac{-98-4i }{74} = \frac{-49}{37} + \frac{-2}{37}i \)
6. \(\frac{-8-6i}{8-4i}= \frac{-8-6i}{8-4i} \cdot \frac{8+4i}{8+4i} = \frac{-64-32i -48 i-24i^2 }{(8)^2-(-4i)^2} = \frac{-64-32i -48 i+24}{64 + 16} = \frac{-40-80i }{80} = \frac{-1}{2} + 1i\)
7. \((7-7i) \cdot (6+3i)= 42+21i -42 i-21i^2 = 42+21i -42 i+21= \color{red}{42+21}\color{blue}{+21i -42i}=\color{red}{63}\color{blue}{-21i}\)
8. \((3-6i)\cdot (-10i)= -30 i+60i^2 = \color{red}{-60}\color{blue}{-30i}\)
9. \((4-10i)-(2-7i)= 4-10i -2+7i =\color{red}{4-2}\color{blue}{-10i +7i}=\color{red}{2}\color{blue}{-3i}\)
10. \((-6+4i) \cdot (-10+3i)= 60-18i -40 i+12i^2 = 60-18i -40 i-12= \color{red}{60-12}\color{blue}{-18i -40i}=\color{red}{48}\color{blue}{-58i}\)
11. \((-10+6i) \cdot (-3+8i)= 30-80i -18 i+48i^2 = 30-80i -18 i-48= \color{red}{30-48}\color{blue}{-80i -18i}=\color{red}{-18}\color{blue}{-98i}\)
12. \((3-6i)\cdot (-10i)= -30 i+60i^2 = \color{red}{-60}\color{blue}{-30i}\)