Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((2-8i)\cdot (-2i)= -4 i+16i^2 = \color{red}{-16}\color{blue}{-4i}\)
2. \((+7i) \cdot (5-2i)= +35 i-14i^2 = \color{red}{14}\color{blue}{+35i}\)
3. \((-2-10i) \cdot (-2-10i)= 4+20i +20 i+100i^2 = 4+20i +20 i-100= \color{red}{4-100}\color{blue}{+20i +20i}=\color{red}{-96}\color{blue}{+40i}\)
4. \((4-3i) \cdot (-3+2i)= -12+8i +9 i-6i^2 = -12+8i +9 i+6= \color{red}{-12+6}\color{blue}{+8i +9i}=\color{red}{-6}\color{blue}{+17i}\)
5. \(\frac{6-i}{-10+10i}= \frac{6-i}{-10+10i} \cdot \frac{-10-10i}{-10-10i} = \frac{-60-60i +10 i+10i^2 }{(-10)^2-(10i)^2} = \frac{-60-60i +10 i-10}{100 + 100} = \frac{-70-50i }{200} = \frac{-7}{20} + \frac{-1}{4}i \)
6. \((4+8i)\cdot (-8i)= -32 i-64i^2 = \color{red}{64}\color{blue}{-32i}\)
7. \((-4+8i) \cdot (9-5i)= -36+20i +72 i-40i^2 = -36+20i +72 i+40= \color{red}{-36+40}\color{blue}{+20i +72i}=\color{red}{4}\color{blue}{+92i}\)
8. \(\frac{-6+7i}{-3-3i}= \frac{-6+7i}{-3-3i} \cdot \frac{-3+3i}{-3+3i} = \frac{18-18i -21 i+21i^2 }{(-3)^2-(-3i)^2} = \frac{18-18i -21 i-21}{9 + 9} = \frac{-3-39i }{18} = \frac{-1}{6} + \frac{-13}{6}i \)
9. \((1+i)+(-2+8i)= 1+i -2+8i =\color{red}{1-2}\color{blue}{+i +8i}=\color{red}{-1}\color{blue}{+9i}\)
10. \((-4-9i)-(-3+2i)= -4-9i +3-2i =\color{red}{-4+3}\color{blue}{-9i -2i}=\color{red}{-1}\color{blue}{-11i}\)
11. \((-4-2i) \cdot (6-7i)= -24+28i -12 i+14i^2 = -24+28i -12 i-14= \color{red}{-24-14}\color{blue}{+28i -12i}=\color{red}{-38}\color{blue}{+16i}\)
12. \((-2-i) \cdot (-2-7i)= 4+14i +2 i+7i^2 = 4+14i +2 i-7= \color{red}{4-7}\color{blue}{+14i +2i}=\color{red}{-3}\color{blue}{+16i}\)