Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-3i)-(4+7i)= -9-3i -4-7i =\color{red}{-9-4}\color{blue}{-3i -7i}=\color{red}{-13}\color{blue}{-10i}\)
2. \((-8-2i)+(-3-2i)= -8-2i -3-2i =\color{red}{-8-3}\color{blue}{-2i -2i}=\color{red}{-11}\color{blue}{-4i}\)
3. \(\frac{7+i}{-7+5i}= \frac{7+i}{-7+5i} \cdot \frac{-7-5i}{-7-5i} = \frac{-49-35i -7 i-5i^2 }{(-7)^2-(5i)^2} = \frac{-49-35i -7 i+5}{49 + 25} = \frac{-44-42i }{74} = \frac{-22}{37} + \frac{-21}{37}i \)
4. \(\frac{10-5i}{-2-i}= \frac{10-5i}{-2-i} \cdot \frac{-2+i}{-2+i} = \frac{-20+10i +10 i-5i^2 }{(-2)^2-(-1i)^2} = \frac{-20+10i +10 i+5}{4 + 1} = \frac{-15+20i }{5} = -3- -4i\)
5. \((4+10i)+(4-2i)= 4+10i +4-2i =\color{red}{4+4}\color{blue}{+10i -2i}=\color{red}{8}\color{blue}{+8i}\)
6. \((-9+4i)+(8-2i)= -9+4i +8-2i =\color{red}{-9+8}\color{blue}{+4i -2i}=\color{red}{-1}\color{blue}{+2i}\)
7. \((-8-10i)+(10+2i)= -8-10i +10+2i =\color{red}{-8+10}\color{blue}{-10i +2i}=\color{red}{2}\color{blue}{-8i}\)
8. \((3-i)+(-1+10i)= 3-i -1+10i =\color{red}{3-1}\color{blue}{-i +10i}=\color{red}{2}\color{blue}{+9i}\)
9. \((3-2i) \cdot (-6+9i)= -18+27i +12 i-18i^2 = -18+27i +12 i+18= \color{red}{-18+18}\color{blue}{+27i +12i}=\color{blue}{39i}\)
10. \((7+5i) \cdot (9+7i)= 63+49i +45 i+35i^2 = 63+49i +45 i-35= \color{red}{63-35}\color{blue}{+49i +45i}=\color{red}{28}\color{blue}{+94i}\)
11. \((9+10i)-(-9+3i)= 9+10i +9-3i =\color{red}{9+9}\color{blue}{+10i -3i}=\color{red}{18}\color{blue}{+7i}\)
12. \((-2+6i)\cdot (-3i)= +6 i-18i^2 = \color{red}{18}\color{blue}{+6i}\)