Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9-i) \cdot (-1+10i)= -9+90i +1 i-10i^2 = -9+90i +1 i+10= \color{red}{-9+10}\color{blue}{+90i +i}=\color{red}{1}\color{blue}{+91i}\)
2. \((-9+3i)\cdot (-8i)= +72 i-24i^2 = \color{red}{24}\color{blue}{+72i}\)
3. \(\frac{-5+4i}{-10+8i}= \frac{-5+4i}{-10+8i} \cdot \frac{-10-8i}{-10-8i} = \frac{50+40i -40 i-32i^2 }{(-10)^2-(8i)^2} = \frac{50+40i -40 i+32}{100 + 64} = \frac{82+0i }{164} = \frac{1}{2} + 0i\)
4. \((5-3i)\cdot (+5i)= +25 i-15i^2 = \color{red}{15}\color{blue}{+25i}\)
5. \(\frac{5-10i}{-4-8i}= \frac{5-10i}{-4-8i} \cdot \frac{-4+8i}{-4+8i} = \frac{-20+40i +40 i-80i^2 }{(-4)^2-(-8i)^2} = \frac{-20+40i +40 i+80}{16 + 64} = \frac{60+80i }{80} = \frac{3}{4} - -1i\)
6. \((-10+7i) \cdot (-6+2i)= 60-20i -42 i+14i^2 = 60-20i -42 i-14= \color{red}{60-14}\color{blue}{-20i -42i}=\color{red}{46}\color{blue}{-62i}\)
7. \(\frac{-8+4i}{-3+4i}= \frac{-8+4i}{-3+4i} \cdot \frac{-3-4i}{-3-4i} = \frac{24+32i -12 i-16i^2 }{(-3)^2-(4i)^2} = \frac{24+32i -12 i+16}{9 + 16} = \frac{40+20i }{25} = \frac{8}{5} - \frac{-4}{5}i \)
8. \((-10-i) \cdot (2+i)= -20-10i -2 i-i^2 = -20-10i -2 i+= \color{red}{-20+1}\color{blue}{-10i -2i}=\color{red}{-19}\color{blue}{-12i}\)
9. \((-1+3i) \cdot (-4+5i)= 4-5i -12 i+15i^2 = 4-5i -12 i-15= \color{red}{4-15}\color{blue}{-5i -12i}=\color{red}{-11}\color{blue}{-17i}\)
10. \((7-5i) \cdot (3+9i)= 21+63i -15 i-45i^2 = 21+63i -15 i+45= \color{red}{21+45}\color{blue}{+63i -15i}=\color{red}{66}\color{blue}{+48i}\)
11. \((-8+3i) \cdot (7+4i)= -56-32i +21 i+12i^2 = -56-32i +21 i-12= \color{red}{-56-12}\color{blue}{-32i +21i}=\color{red}{-68}\color{blue}{-11i}\)
12. \((-9+5i)\cdot (-5i)= +45 i-25i^2 = \color{red}{25}\color{blue}{+45i}\)