Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5-i)\cdot (+7i)= +35 i-7i^2 = \color{red}{7}\color{blue}{+35i}\)
2. \((-5-3i) \cdot (6-8i)= -30+40i -18 i+24i^2 = -30+40i -18 i-24= \color{red}{-30-24}\color{blue}{+40i -18i}=\color{red}{-54}\color{blue}{+22i}\)
3. \((-10+6i)+(-7+8i)= -10+6i -7+8i =\color{red}{-10-7}\color{blue}{+6i +8i}=\color{red}{-17}\color{blue}{+14i}\)
4. \(\frac{6+5i}{10+9i}= \frac{6+5i}{10+9i} \cdot \frac{10-9i}{10-9i} = \frac{60-54i +50 i-45i^2 }{(10)^2-(9i)^2} = \frac{60-54i +50 i+45}{100 + 81} = \frac{105-4i }{181} = \frac{105}{181} + \frac{-4}{181}i \)
5. \(\frac{10-5i}{-7+7i}= \frac{10-5i}{-7+7i} \cdot \frac{-7-7i}{-7-7i} = \frac{-70-70i +35 i+35i^2 }{(-7)^2-(7i)^2} = \frac{-70-70i +35 i-35}{49 + 49} = \frac{-105-35i }{98} = \frac{-15}{14} + \frac{-5}{14}i \)
6. \((+5i) \cdot (-2-10i)= -10 i-50i^2 = \color{red}{50}\color{blue}{-10i}\)
7. \((+8i) \cdot (-8-2i)= -64 i-16i^2 = \color{red}{16}\color{blue}{-64i}\)
8. \((-9-9i)+(8+10i)= -9-9i +8+10i =\color{red}{-9+8}\color{blue}{-9i +10i}=\color{red}{-1}\color{blue}{+i}\)
9. \((-4+i) \cdot (5+3i)= -20-12i +5 i+3i^2 = -20-12i +5 i-3= \color{red}{-20-3}\color{blue}{-12i +5i}=\color{red}{-23}\color{blue}{-7i}\)
10. \((-9+2i)+(7+5i)= -9+2i +7+5i =\color{red}{-9+7}\color{blue}{+2i +5i}=\color{red}{-2}\color{blue}{+7i}\)
11. \((8+7i) \cdot (-4-2i)= -32-16i -28 i-14i^2 = -32-16i -28 i+14= \color{red}{-32+14}\color{blue}{-16i -28i}=\color{red}{-18}\color{blue}{-44i}\)
12. \(\frac{-4-10i}{-1+9i}= \frac{-4-10i}{-1+9i} \cdot \frac{-1-9i}{-1-9i} = \frac{4+36i +10 i+90i^2 }{(-1)^2-(9i)^2} = \frac{4+36i +10 i-90}{1 + 81} = \frac{-86+46i }{82} = \frac{-43}{41} - \frac{-23}{41}i \)