Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+3i)+(-5-9i)= -4+3i -5-9i =\color{red}{-4-5}\color{blue}{+3i -9i}=\color{red}{-9}\color{blue}{-6i}\)
2. \((-10+3i) \cdot (2+3i)= -20-30i +6 i+9i^2 = -20-30i +6 i-9= \color{red}{-20-9}\color{blue}{-30i +6i}=\color{red}{-29}\color{blue}{-24i}\)
3. \((7-3i)\cdot (-7i)= -49 i+21i^2 = \color{red}{-21}\color{blue}{-49i}\)
4. \((-3-2i)\cdot (-2i)= +6 i+4i^2 = \color{red}{-4}\color{blue}{+6i}\)
5. \((5+8i)+(3-9i)= 5+8i +3-9i =\color{red}{5+3}\color{blue}{+8i -9i}=\color{red}{8}\color{blue}{-i}\)
6. \((7-9i) \cdot (6+4i)= 42+28i -54 i-36i^2 = 42+28i -54 i+36= \color{red}{42+36}\color{blue}{+28i -54i}=\color{red}{78}\color{blue}{-26i}\)
7. \((3+4i)\cdot (+4i)= +12 i+16i^2 = \color{red}{-16}\color{blue}{+12i}\)
8. \((-8-3i)-(3+8i)= -8-3i -3-8i =\color{red}{-8-3}\color{blue}{-3i -8i}=\color{red}{-11}\color{blue}{-11i}\)
9. \((9+9i)\cdot (+5i)= +45 i+45i^2 = \color{red}{-45}\color{blue}{+45i}\)
10. \((-6-5i)+(1-10i)= -6-5i +1-10i =\color{red}{-6+1}\color{blue}{-5i -10i}=\color{red}{-5}\color{blue}{-15i}\)
11. \(\frac{-9+2i}{5+5i}= \frac{-9+2i}{5+5i} \cdot \frac{5-5i}{5-5i} = \frac{-45+45i +10 i-10i^2 }{(5)^2-(5i)^2} = \frac{-45+45i +10 i+10}{25 + 25} = \frac{-35+55i }{50} = \frac{-7}{10} - \frac{-11}{10}i \)
12. \((1-10i) \cdot (-2-7i)= -2-7i +20 i+70i^2 = -2-7i +20 i-70= \color{red}{-2-70}\color{blue}{-7i +20i}=\color{red}{-72}\color{blue}{+13i}\)