Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((6-10i)+(9+5i)= 6-10i +9+5i =\color{red}{6+9}\color{blue}{-10i +5i}=\color{red}{15}\color{blue}{-5i}\)
2. \((-7+3i)-(2-9i)= -7+3i -2+9i =\color{red}{-7-2}\color{blue}{+3i +9i}=\color{red}{-9}\color{blue}{+12i}\)
3. \(\frac{4+2i}{-9+6i}= \frac{4+2i}{-9+6i} \cdot \frac{-9-6i}{-9-6i} = \frac{-36-24i -18 i-12i^2 }{(-9)^2-(6i)^2} = \frac{-36-24i -18 i+12}{81 + 36} = \frac{-24-42i }{117} = \frac{-8}{39} + \frac{-14}{39}i \)
4. \((5+2i) \cdot (8+10i)= 40+50i +16 i+20i^2 = 40+50i +16 i-20= \color{red}{40-20}\color{blue}{+50i +16i}=\color{red}{20}\color{blue}{+66i}\)
5. \((9-4i)-(5+i)= 9-4i -5-i =\color{red}{9-5}\color{blue}{-4i -i}=\color{red}{4}\color{blue}{-5i}\)
6. \((-6+3i)+(-7-i)= -6+3i -7-i =\color{red}{-6-7}\color{blue}{+3i -i}=\color{red}{-13}\color{blue}{+2i}\)
7. \(\frac{-2+8i}{5-3i}= \frac{-2+8i}{5-3i} \cdot \frac{5+3i}{5+3i} = \frac{-10-6i +40 i+24i^2 }{(5)^2-(-3i)^2} = \frac{-10-6i +40 i-24}{25 + 9} = \frac{-34+34i }{34} = -1- -1i\)
8. \(\frac{-1-5i}{1+10i}= \frac{-1-5i}{1+10i} \cdot \frac{1-10i}{1-10i} = \frac{-1+10i -5 i+50i^2 }{(1)^2-(10i)^2} = \frac{-1+10i -5 i-50}{1 + 100} = \frac{-51+5i }{101} = \frac{-51}{101} - \frac{-5}{101}i \)
9. \((-1+7i)+(5-2i)= -1+7i +5-2i =\color{red}{-1+5}\color{blue}{+7i -2i}=\color{red}{4}\color{blue}{+5i}\)
10. \((-3-10i) \cdot (7+8i)= -21-24i -70 i-80i^2 = -21-24i -70 i+80= \color{red}{-21+80}\color{blue}{-24i -70i}=\color{red}{59}\color{blue}{-94i}\)
11. \((-7i) \cdot (6+10i)= -42 i-70i^2 = \color{red}{70}\color{blue}{-42i}\)
12. \((5-7i)+(-9+3i)= 5-7i -9+3i =\color{red}{5-9}\color{blue}{-7i +3i}=\color{red}{-4}\color{blue}{-4i}\)