Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((1+8i)-(-4+8i)= 1+8i +4-8i =\color{red}{1+4}\color{blue}{+8i -8i}=\color{red}{5}\)
2. \((10+4i)-(-1-5i)= 10+4i +1+5i =\color{red}{10+1}\color{blue}{+4i +5i}=\color{red}{11}\color{blue}{+9i}\)
3. \((3+6i)+(-7-i)= 3+6i -7-i =\color{red}{3-7}\color{blue}{+6i -i}=\color{red}{-4}\color{blue}{+5i}\)
4. \((-3+7i)\cdot (+9i)= -27 i+63i^2 = \color{red}{-63}\color{blue}{-27i}\)
5. \((-1-5i) \cdot (-9+i)= 9-i +45 i-5i^2 = 9-i +45 i+5= \color{red}{9+5}\color{blue}{-i +45i}=\color{red}{14}\color{blue}{+44i}\)
6. \((9+i)+(-5+4i)= 9+i -5+4i =\color{red}{9-5}\color{blue}{+i +4i}=\color{red}{4}\color{blue}{+5i}\)
7. \((-6-7i) \cdot (-9+9i)= 54-54i +63 i-63i^2 = 54-54i +63 i+63= \color{red}{54+63}\color{blue}{-54i +63i}=\color{red}{117}\color{blue}{+9i}\)
8. \(\frac{10+7i}{10+3i}= \frac{10+7i}{10+3i} \cdot \frac{10-3i}{10-3i} = \frac{100-30i +70 i-21i^2 }{(10)^2-(3i)^2} = \frac{100-30i +70 i+21}{100 + 9} = \frac{121+40i }{109} = \frac{121}{109} - \frac{-40}{109}i \)
9. \((-9+7i)-(6+10i)= -9+7i -6-10i =\color{red}{-9-6}\color{blue}{+7i -10i}=\color{red}{-15}\color{blue}{-3i}\)
10. \((-4+i) \cdot (-6-9i)= 24+36i -6 i-9i^2 = 24+36i -6 i+9= \color{red}{24+9}\color{blue}{+36i -6i}=\color{red}{33}\color{blue}{+30i}\)
11. \((-6-4i)-(-8+2i)= -6-4i +8-2i =\color{red}{-6+8}\color{blue}{-4i -2i}=\color{red}{2}\color{blue}{-6i}\)
12. \((10-10i)+(-2-10i)= 10-10i -2-10i =\color{red}{10-2}\color{blue}{-10i -10i}=\color{red}{8}\color{blue}{-20i}\)