Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10+7i) \cdot (-3+i)= -30+10i -21 i+7i^2 = -30+10i -21 i-7= \color{red}{-30-7}\color{blue}{+10i -21i}=\color{red}{-37}\color{blue}{-11i}\)
2. \((-6i) \cdot (6+10i)= -36 i-60i^2 = \color{red}{60}\color{blue}{-36i}\)
3. \((-1+i)\cdot (-10i)= +10 i-10i^2 = \color{red}{10}\color{blue}{+10i}\)
4. \((+5i) \cdot (-5-4i)= -25 i-20i^2 = \color{red}{20}\color{blue}{-25i}\)
5. \((5-6i) \cdot (3+4i)= 15+20i -18 i-24i^2 = 15+20i -18 i+24= \color{red}{15+24}\color{blue}{+20i -18i}=\color{red}{39}\color{blue}{+2i}\)
6. \((10-3i) \cdot (-3+7i)= -30+70i +9 i-21i^2 = -30+70i +9 i+21= \color{red}{-30+21}\color{blue}{+70i +9i}=\color{red}{-9}\color{blue}{+79i}\)
7. \((-3-2i)\cdot (+10i)= -30 i-20i^2 = \color{red}{20}\color{blue}{-30i}\)
8. \((7+8i) \cdot (3-5i)= 21-35i +24 i-40i^2 = 21-35i +24 i+40= \color{red}{21+40}\color{blue}{-35i +24i}=\color{red}{61}\color{blue}{-11i}\)
9. \((7-7i) \cdot (-6+9i)= -42+63i +42 i-63i^2 = -42+63i +42 i+63= \color{red}{-42+63}\color{blue}{+63i +42i}=\color{red}{21}\color{blue}{+105i}\)
10. \((-8-5i) \cdot (-7+6i)= 56-48i +35 i-30i^2 = 56-48i +35 i+30= \color{red}{56+30}\color{blue}{-48i +35i}=\color{red}{86}\color{blue}{-13i}\)
11. \((7+4i) \cdot (-7-3i)= -49-21i -28 i-12i^2 = -49-21i -28 i+12= \color{red}{-49+12}\color{blue}{-21i -28i}=\color{red}{-37}\color{blue}{-49i}\)
12. \((-4+8i) \cdot (-4-3i)= 16+12i -32 i-24i^2 = 16+12i -32 i+24= \color{red}{16+24}\color{blue}{+12i -32i}=\color{red}{40}\color{blue}{-20i}\)