Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-9i)+(2+5i)= -4-9i +2+5i =\color{red}{-4+2}\color{blue}{-9i +5i}=\color{red}{-2}\color{blue}{-4i}\)
2. \((10+10i) \cdot (5+7i)= 50+70i +50 i+70i^2 = 50+70i +50 i-70= \color{red}{50-70}\color{blue}{+70i +50i}=\color{red}{-20}\color{blue}{+120i}\)
3. \(\frac{5+5i}{6-3i}= \frac{5+5i}{6-3i} \cdot \frac{6+3i}{6+3i} = \frac{30+15i +30 i+15i^2 }{(6)^2-(-3i)^2} = \frac{30+15i +30 i-15}{36 + 9} = \frac{15+45i }{45} = \frac{1}{3} - -1i\)
4. \((-5+6i)+(-2+4i)= -5+6i -2+4i =\color{red}{-5-2}\color{blue}{+6i +4i}=\color{red}{-7}\color{blue}{+10i}\)
5. \((-7-9i)-(6-8i)= -7-9i -6+8i =\color{red}{-7-6}\color{blue}{-9i +8i}=\color{red}{-13}\color{blue}{-i}\)
6. \((3+9i)-(10+7i)= 3+9i -10-7i =\color{red}{3-10}\color{blue}{+9i -7i}=\color{red}{-7}\color{blue}{+2i}\)
7. \((6-4i)+(-4+9i)= 6-4i -4+9i =\color{red}{6-4}\color{blue}{-4i +9i}=\color{red}{2}\color{blue}{+5i}\)
8. \((10+10i)\cdot (+7i)= +70 i+70i^2 = \color{red}{-70}\color{blue}{+70i}\)
9. \((-10-2i) \cdot (-8+4i)= 80-40i +16 i-8i^2 = 80-40i +16 i+8= \color{red}{80+8}\color{blue}{-40i +16i}=\color{red}{88}\color{blue}{-24i}\)
10. \((-4-4i)+(5-6i)= -4-4i +5-6i =\color{red}{-4+5}\color{blue}{-4i -6i}=\color{red}{1}\color{blue}{-10i}\)
11. \((-8-4i) \cdot (-9-5i)= 72+40i +36 i+20i^2 = 72+40i +36 i-20= \color{red}{72-20}\color{blue}{+40i +36i}=\color{red}{52}\color{blue}{+76i}\)
12. \(\frac{-10+9i}{10+3i}= \frac{-10+9i}{10+3i} \cdot \frac{10-3i}{10-3i} = \frac{-100+30i +90 i-27i^2 }{(10)^2-(3i)^2} = \frac{-100+30i +90 i+27}{100 + 9} = \frac{-73+120i }{109} = \frac{-73}{109} - \frac{-120}{109}i \)