Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9+8i)-(-6-4i)= 9+8i +6+4i =\color{red}{9+6}\color{blue}{+8i +4i}=\color{red}{15}\color{blue}{+12i}\)
2. \(\frac{3+10i}{1-10i}= \frac{3+10i}{1-10i} \cdot \frac{1+10i}{1+10i} = \frac{3+30i +10 i+100i^2 }{(1)^2-(-10i)^2} = \frac{3+30i +10 i-100}{1 + 100} = \frac{-97+40i }{101} = \frac{-97}{101} - \frac{-40}{101}i \)
3. \((-2i) \cdot (8+10i)= -16 i-20i^2 = \color{red}{20}\color{blue}{-16i}\)
4. \(\frac{-8+4i}{-8-10i}= \frac{-8+4i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{64-80i -32 i+40i^2 }{(-8)^2-(-10i)^2} = \frac{64-80i -32 i-40}{64 + 100} = \frac{24-112i }{164} = \frac{6}{41} + \frac{-28}{41}i \)
5. \(\frac{-1-10i}{9-2i}= \frac{-1-10i}{9-2i} \cdot \frac{9+2i}{9+2i} = \frac{-9-2i -90 i-20i^2 }{(9)^2-(-2i)^2} = \frac{-9-2i -90 i+20}{81 + 4} = \frac{11-92i }{85} = \frac{11}{85} + \frac{-92}{85}i \)
6. \(\frac{3-6i}{-5-4i}= \frac{3-6i}{-5-4i} \cdot \frac{-5+4i}{-5+4i} = \frac{-15+12i +30 i-24i^2 }{(-5)^2-(-4i)^2} = \frac{-15+12i +30 i+24}{25 + 16} = \frac{9+42i }{41} = \frac{9}{41} - \frac{-42}{41}i \)
7. \((-10i) \cdot (1+4i)= -10 i-40i^2 = \color{red}{40}\color{blue}{-10i}\)
8. \(\frac{-10-10i}{3-2i}= \frac{-10-10i}{3-2i} \cdot \frac{3+2i}{3+2i} = \frac{-30-20i -30 i-20i^2 }{(3)^2-(-2i)^2} = \frac{-30-20i -30 i+20}{9 + 4} = \frac{-10-50i }{13} = \frac{-10}{13} + \frac{-50}{13}i \)
9. \((-5-5i) \cdot (4-10i)= -20+50i -20 i+50i^2 = -20+50i -20 i-50= \color{red}{-20-50}\color{blue}{+50i -20i}=\color{red}{-70}\color{blue}{+30i}\)
10. \((-8+5i) \cdot (7-5i)= -56+40i +35 i-25i^2 = -56+40i +35 i+25= \color{red}{-56+25}\color{blue}{+40i +35i}=\color{red}{-31}\color{blue}{+75i}\)
11. \((-6+7i) \cdot (10+2i)= -60-12i +70 i+14i^2 = -60-12i +70 i-14= \color{red}{-60-14}\color{blue}{-12i +70i}=\color{red}{-74}\color{blue}{+58i}\)
12. \((4+9i)-(-5-5i)= 4+9i +5+5i =\color{red}{4+5}\color{blue}{+9i +5i}=\color{red}{9}\color{blue}{+14i}\)