Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+7i)-(3+6i)= -4+7i -3-6i =\color{red}{-4-3}\color{blue}{+7i -6i}=\color{red}{-7}\color{blue}{+i}\)
2. \((2-9i)\cdot (+8i)= +16 i-72i^2 = \color{red}{72}\color{blue}{+16i}\)
3. \((10-6i) \cdot (6+9i)= 60+90i -36 i-54i^2 = 60+90i -36 i+54= \color{red}{60+54}\color{blue}{+90i -36i}=\color{red}{114}\color{blue}{+54i}\)
4. \((-9+2i)+(-9-3i)= -9+2i -9-3i =\color{red}{-9-9}\color{blue}{+2i -3i}=\color{red}{-18}\color{blue}{-i}\)
5. \((-5+6i) \cdot (3-5i)= -15+25i +18 i-30i^2 = -15+25i +18 i+30= \color{red}{-15+30}\color{blue}{+25i +18i}=\color{red}{15}\color{blue}{+43i}\)
6. \(\frac{7+10i}{-9+7i}= \frac{7+10i}{-9+7i} \cdot \frac{-9-7i}{-9-7i} = \frac{-63-49i -90 i-70i^2 }{(-9)^2-(7i)^2} = \frac{-63-49i -90 i+70}{81 + 49} = \frac{7-139i }{130} = \frac{7}{130} + \frac{-139}{130}i \)
7. \((+9i) \cdot (-2-10i)= -18 i-90i^2 = \color{red}{90}\color{blue}{-18i}\)
8. \((10-10i)+(3+i)= 10-10i +3+i =\color{red}{10+3}\color{blue}{-10i +i}=\color{red}{13}\color{blue}{-9i}\)
9. \((-3+3i) \cdot (-8-i)= 24+3i -24 i-3i^2 = 24+3i -24 i+3= \color{red}{24+3}\color{blue}{+3i -24i}=\color{red}{27}\color{blue}{-21i}\)
10. \(\frac{2+7i}{-1-6i}= \frac{2+7i}{-1-6i} \cdot \frac{-1+6i}{-1+6i} = \frac{-2+12i -7 i+42i^2 }{(-1)^2-(-6i)^2} = \frac{-2+12i -7 i-42}{1 + 36} = \frac{-44+5i }{37} = \frac{-44}{37} - \frac{-5}{37}i \)
11. \((+8i) \cdot (6+8i)= +48 i+64i^2 = \color{red}{-64}\color{blue}{+48i}\)
12. \((6+9i) \cdot (4+10i)= 24+60i +36 i+90i^2 = 24+60i +36 i-90= \color{red}{24-90}\color{blue}{+60i +36i}=\color{red}{-66}\color{blue}{+96i}\)