Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7+5i)-(-8-10i)= 7+5i +8+10i =\color{red}{7+8}\color{blue}{+5i +10i}=\color{red}{15}\color{blue}{+15i}\)
2. \((-4-6i)\cdot (+6i)= -24 i-36i^2 = \color{red}{36}\color{blue}{-24i}\)
3. \((-7+4i)\cdot (+i)= -7 i+4i^2 = \color{red}{-4}\color{blue}{-7i}\)
4. \(\frac{-9-9i}{-9+9i}= \frac{-9-9i}{-9+9i} \cdot \frac{-9-9i}{-9-9i} = \frac{81+81i +81 i+81i^2 }{(-9)^2-(9i)^2} = \frac{81+81i +81 i-81}{81 + 81} = \frac{0+162i }{162} = 0- -1i\)
5. \((4-5i)-(7-4i)= 4-5i -7+4i =\color{red}{4-7}\color{blue}{-5i +4i}=\color{red}{-3}\color{blue}{-i}\)
6. \((1+3i)-(3-5i)= 1+3i -3+5i =\color{red}{1-3}\color{blue}{+3i +5i}=\color{red}{-2}\color{blue}{+8i}\)
7. \((-2-2i)\cdot (-7i)= +14 i+14i^2 = \color{red}{-14}\color{blue}{+14i}\)
8. \((-1-6i)+(-9-i)= -1-6i -9-i =\color{red}{-1-9}\color{blue}{-6i -i}=\color{red}{-10}\color{blue}{-7i}\)
9. \((9-4i)-(10+4i)= 9-4i -10-4i =\color{red}{9-10}\color{blue}{-4i -4i}=\color{red}{-1}\color{blue}{-8i}\)
10. \((-6-5i)+(-3+9i)= -6-5i -3+9i =\color{red}{-6-3}\color{blue}{-5i +9i}=\color{red}{-9}\color{blue}{+4i}\)
11. \(\frac{-1+7i}{6+2i}= \frac{-1+7i}{6+2i} \cdot \frac{6-2i}{6-2i} = \frac{-6+2i +42 i-14i^2 }{(6)^2-(2i)^2} = \frac{-6+2i +42 i+14}{36 + 4} = \frac{8+44i }{40} = \frac{1}{5} - \frac{-11}{10}i \)
12. \(\frac{-7+7i}{-7-10i}= \frac{-7+7i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{49-70i -49 i+70i^2 }{(-7)^2-(-10i)^2} = \frac{49-70i -49 i-70}{49 + 100} = \frac{-21-119i }{149} = \frac{-21}{149} + \frac{-119}{149}i \)