Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8-4i}{-8-6i}= \frac{8-4i}{-8-6i} \cdot \frac{-8+6i}{-8+6i} = \frac{-64+48i +32 i-24i^2 }{(-8)^2-(-6i)^2} = \frac{-64+48i +32 i+24}{64 + 36} = \frac{-40+80i }{100} = \frac{-2}{5} - \frac{-4}{5}i \)
2. \((-7-8i)\cdot (-9i)= +63 i+72i^2 = \color{red}{-72}\color{blue}{+63i}\)
3. \(\frac{2+5i}{-8-2i}= \frac{2+5i}{-8-2i} \cdot \frac{-8+2i}{-8+2i} = \frac{-16+4i -40 i+10i^2 }{(-8)^2-(-2i)^2} = \frac{-16+4i -40 i-10}{64 + 4} = \frac{-26-36i }{68} = \frac{-13}{34} + \frac{-9}{17}i \)
4. \(\frac{-7-3i}{-8-10i}= \frac{-7-3i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{56-70i +24 i-30i^2 }{(-8)^2-(-10i)^2} = \frac{56-70i +24 i+30}{64 + 100} = \frac{86-46i }{164} = \frac{43}{82} + \frac{-23}{82}i \)
5. \((8+9i)+(1-10i)= 8+9i +1-10i =\color{red}{8+1}\color{blue}{+9i -10i}=\color{red}{9}\color{blue}{-i}\)
6. \((8-3i) \cdot (6-i)= 48-8i -18 i+3i^2 = 48-8i -18 i-3= \color{red}{48-3}\color{blue}{-8i -18i}=\color{red}{45}\color{blue}{-26i}\)
7. \((2+7i)+(9-5i)= 2+7i +9-5i =\color{red}{2+9}\color{blue}{+7i -5i}=\color{red}{11}\color{blue}{+2i}\)
8. \(\frac{-10+3i}{3-5i}= \frac{-10+3i}{3-5i} \cdot \frac{3+5i}{3+5i} = \frac{-30-50i +9 i+15i^2 }{(3)^2-(-5i)^2} = \frac{-30-50i +9 i-15}{9 + 25} = \frac{-45-41i }{34} = \frac{-45}{34} + \frac{-41}{34}i \)
9. \((7+2i) \cdot (6+9i)= 42+63i +12 i+18i^2 = 42+63i +12 i-18= \color{red}{42-18}\color{blue}{+63i +12i}=\color{red}{24}\color{blue}{+75i}\)
10. \((1+7i)-(-8+7i)= 1+7i +8-7i =\color{red}{1+8}\color{blue}{+7i -7i}=\color{red}{9}\)
11. \((-1-i)+(1+5i)= -1-i +1+5i =\color{red}{-1+1}\color{blue}{-i +5i}=\color{blue}{4i}\)
12. \(\frac{10-5i}{-10+7i}= \frac{10-5i}{-10+7i} \cdot \frac{-10-7i}{-10-7i} = \frac{-100-70i +50 i+35i^2 }{(-10)^2-(7i)^2} = \frac{-100-70i +50 i-35}{100 + 49} = \frac{-135-20i }{149} = \frac{-135}{149} + \frac{-20}{149}i \)