Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+8i)-(5+4i)= -1+8i -5-4i =\color{red}{-1-5}\color{blue}{+8i -4i}=\color{red}{-6}\color{blue}{+4i}\)
2. \(\frac{10-9i}{6+8i}= \frac{10-9i}{6+8i} \cdot \frac{6-8i}{6-8i} = \frac{60-80i -54 i+72i^2 }{(6)^2-(8i)^2} = \frac{60-80i -54 i-72}{36 + 64} = \frac{-12-134i }{100} = \frac{-3}{25} + \frac{-67}{50}i \)
3. \(\frac{9+4i}{-7+9i}= \frac{9+4i}{-7+9i} \cdot \frac{-7-9i}{-7-9i} = \frac{-63-81i -28 i-36i^2 }{(-7)^2-(9i)^2} = \frac{-63-81i -28 i+36}{49 + 81} = \frac{-27-109i }{130} = \frac{-27}{130} + \frac{-109}{130}i \)
4. \((-3+i)+(-7+7i)= -3+i -7+7i =\color{red}{-3-7}\color{blue}{+i +7i}=\color{red}{-10}\color{blue}{+8i}\)
5. \((-1+10i) \cdot (9-7i)= -9+7i +90 i-70i^2 = -9+7i +90 i+70= \color{red}{-9+70}\color{blue}{+7i +90i}=\color{red}{61}\color{blue}{+97i}\)
6. \((-1+6i) \cdot (6+8i)= -6-8i +36 i+48i^2 = -6-8i +36 i-48= \color{red}{-6-48}\color{blue}{-8i +36i}=\color{red}{-54}\color{blue}{+28i}\)
7. \((6+i)-(10-i)= 6+i -10+i =\color{red}{6-10}\color{blue}{+i +i}=\color{red}{-4}\color{blue}{+2i}\)
8. \((-10+3i)-(-6-9i)= -10+3i +6+9i =\color{red}{-10+6}\color{blue}{+3i +9i}=\color{red}{-4}\color{blue}{+12i}\)
9. \(\frac{1-5i}{3+8i}= \frac{1-5i}{3+8i} \cdot \frac{3-8i}{3-8i} = \frac{3-8i -15 i+40i^2 }{(3)^2-(8i)^2} = \frac{3-8i -15 i-40}{9 + 64} = \frac{-37-23i }{73} = \frac{-37}{73} + \frac{-23}{73}i \)
10. \(\frac{-4-i}{-4-10i}= \frac{-4-i}{-4-10i} \cdot \frac{-4+10i}{-4+10i} = \frac{16-40i +4 i-10i^2 }{(-4)^2-(-10i)^2} = \frac{16-40i +4 i+10}{16 + 100} = \frac{26-36i }{116} = \frac{13}{58} + \frac{-9}{29}i \)
11. \((-2-5i) \cdot (-6-i)= 12+2i +30 i+5i^2 = 12+2i +30 i-5= \color{red}{12-5}\color{blue}{+2i +30i}=\color{red}{7}\color{blue}{+32i}\)
12. \((8+4i) \cdot (-7-8i)= -56-64i -28 i-32i^2 = -56-64i -28 i+32= \color{red}{-56+32}\color{blue}{-64i -28i}=\color{red}{-24}\color{blue}{-92i}\)