Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-6+5i}{1-3i}= \frac{-6+5i}{1-3i} \cdot \frac{1+3i}{1+3i} = \frac{-6-18i +5 i+15i^2 }{(1)^2-(-3i)^2} = \frac{-6-18i +5 i-15}{1 + 9} = \frac{-21-13i }{10} = \frac{-21}{10} + \frac{-13}{10}i \)
2. \(\frac{-6+6i}{3-i}= \frac{-6+6i}{3-i} \cdot \frac{3+i}{3+i} = \frac{-18-6i +18 i+6i^2 }{(3)^2-(-1i)^2} = \frac{-18-6i +18 i-6}{9 + 1} = \frac{-24+12i }{10} = \frac{-12}{5} - \frac{-6}{5}i \)
3. \((-7-3i) \cdot (1-5i)= -7+35i -3 i+15i^2 = -7+35i -3 i-15= \color{red}{-7-15}\color{blue}{+35i -3i}=\color{red}{-22}\color{blue}{+32i}\)
4. \((8-8i) \cdot (6+2i)= 48+16i -48 i-16i^2 = 48+16i -48 i+16= \color{red}{48+16}\color{blue}{+16i -48i}=\color{red}{64}\color{blue}{-32i}\)
5. \((-9+2i)-(3-4i)= -9+2i -3+4i =\color{red}{-9-3}\color{blue}{+2i +4i}=\color{red}{-12}\color{blue}{+6i}\)
6. \((3+3i) \cdot (-8-4i)= -24-12i -24 i-12i^2 = -24-12i -24 i+12= \color{red}{-24+12}\color{blue}{-12i -24i}=\color{red}{-12}\color{blue}{-36i}\)
7. \((-8+9i)+(-4+4i)= -8+9i -4+4i =\color{red}{-8-4}\color{blue}{+9i +4i}=\color{red}{-12}\color{blue}{+13i}\)
8. \((1-3i)-(3-4i)= 1-3i -3+4i =\color{red}{1-3}\color{blue}{-3i +4i}=\color{red}{-2}\color{blue}{+i}\)
9. \((-1+8i) \cdot (6-3i)= -6+3i +48 i-24i^2 = -6+3i +48 i+24= \color{red}{-6+24}\color{blue}{+3i +48i}=\color{red}{18}\color{blue}{+51i}\)
10. \(\frac{-5-5i}{9+2i}= \frac{-5-5i}{9+2i} \cdot \frac{9-2i}{9-2i} = \frac{-45+10i -45 i+10i^2 }{(9)^2-(2i)^2} = \frac{-45+10i -45 i-10}{81 + 4} = \frac{-55-35i }{85} = \frac{-11}{17} + \frac{-7}{17}i \)
11. \((-8-5i) \cdot (9-8i)= -72+64i -45 i+40i^2 = -72+64i -45 i-40= \color{red}{-72-40}\color{blue}{+64i -45i}=\color{red}{-112}\color{blue}{+19i}\)
12. \((6+6i) \cdot (9-3i)= 54-18i +54 i-18i^2 = 54-18i +54 i+18= \color{red}{54+18}\color{blue}{-18i +54i}=\color{red}{72}\color{blue}{+36i}\)