Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-3+3i}{-9-7i}= \frac{-3+3i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{27-21i -27 i+21i^2 }{(-9)^2-(-7i)^2} = \frac{27-21i -27 i-21}{81 + 49} = \frac{6-48i }{130} = \frac{3}{65} + \frac{-24}{65}i \)
2. \((4-7i) \cdot (9+8i)= 36+32i -63 i-56i^2 = 36+32i -63 i+56= \color{red}{36+56}\color{blue}{+32i -63i}=\color{red}{92}\color{blue}{-31i}\)
3. \(\frac{2+5i}{1+7i}= \frac{2+5i}{1+7i} \cdot \frac{1-7i}{1-7i} = \frac{2-14i +5 i-35i^2 }{(1)^2-(7i)^2} = \frac{2-14i +5 i+35}{1 + 49} = \frac{37-9i }{50} = \frac{37}{50} + \frac{-9}{50}i \)
4. \((-9i) \cdot (-1-3i)= +9 i+27i^2 = \color{red}{-27}\color{blue}{+9i}\)
5. \((6+7i) \cdot (9-4i)= 54-24i +63 i-28i^2 = 54-24i +63 i+28= \color{red}{54+28}\color{blue}{-24i +63i}=\color{red}{82}\color{blue}{+39i}\)
6. \(\frac{4+9i}{3+6i}= \frac{4+9i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{12-24i +27 i-54i^2 }{(3)^2-(6i)^2} = \frac{12-24i +27 i+54}{9 + 36} = \frac{66+3i }{45} = \frac{22}{15} - \frac{-1}{15}i \)
7. \((-6+9i) \cdot (1-10i)= -6+60i +9 i-90i^2 = -6+60i +9 i+90= \color{red}{-6+90}\color{blue}{+60i +9i}=\color{red}{84}\color{blue}{+69i}\)
8. \(\frac{-8+8i}{-8+8i}= \frac{-8+8i}{-8+8i} \cdot \frac{-8-8i}{-8-8i} = \frac{64+64i -64 i-64i^2 }{(-8)^2-(8i)^2} = \frac{64+64i -64 i+64}{64 + 64} = \frac{128+0i }{128} = 1+ 0i\)
9. \((-4+10i)\cdot (-i)= +4 i-10i^2 = \color{red}{10}\color{blue}{+4i}\)
10. \((9-7i)\cdot (+i)= +9 i-7i^2 = \color{red}{7}\color{blue}{+9i}\)
11. \((-2+6i)\cdot (-10i)= +20 i-60i^2 = \color{red}{60}\color{blue}{+20i}\)
12. \((-1+2i) \cdot (4-8i)= -4+8i +8 i-16i^2 = -4+8i +8 i+16= \color{red}{-4+16}\color{blue}{+8i +8i}=\color{red}{12}\color{blue}{+16i}\)