Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+9i)+(-9-i)= -6+9i -9-i =\color{red}{-6-9}\color{blue}{+9i -i}=\color{red}{-15}\color{blue}{+8i}\)
2. \((+3i) \cdot (8+2i)= +24 i+6i^2 = \color{red}{-6}\color{blue}{+24i}\)
3. \((+9i) \cdot (1+5i)= +9 i+45i^2 = \color{red}{-45}\color{blue}{+9i}\)
4. \((-6+6i)+(-1-7i)= -6+6i -1-7i =\color{red}{-6-1}\color{blue}{+6i -7i}=\color{red}{-7}\color{blue}{-i}\)
5. \((5-2i)\cdot (+7i)= +35 i-14i^2 = \color{red}{14}\color{blue}{+35i}\)
6. \((4+i)+(-10-5i)= 4+i -10-5i =\color{red}{4-10}\color{blue}{+i -5i}=\color{red}{-6}\color{blue}{-4i}\)
7. \((2+7i)+(-3+2i)= 2+7i -3+2i =\color{red}{2-3}\color{blue}{+7i +2i}=\color{red}{-1}\color{blue}{+9i}\)
8. \(\frac{7+3i}{10-9i}= \frac{7+3i}{10-9i} \cdot \frac{10+9i}{10+9i} = \frac{70+63i +30 i+27i^2 }{(10)^2-(-9i)^2} = \frac{70+63i +30 i-27}{100 + 81} = \frac{43+93i }{181} = \frac{43}{181} - \frac{-93}{181}i \)
9. \((9+4i)+(-5-10i)= 9+4i -5-10i =\color{red}{9-5}\color{blue}{+4i -10i}=\color{red}{4}\color{blue}{-6i}\)
10. \((+9i) \cdot (4-6i)= +36 i-54i^2 = \color{red}{54}\color{blue}{+36i}\)
11. \((9-i) \cdot (-2+7i)= -18+63i +2 i-7i^2 = -18+63i +2 i+7= \color{red}{-18+7}\color{blue}{+63i +2i}=\color{red}{-11}\color{blue}{+65i}\)
12. \((7+2i) \cdot (-2-7i)= -14-49i -4 i-14i^2 = -14-49i -4 i+14= \color{red}{-14+14}\color{blue}{-49i -4i}=\color{blue}{-53i}\)