Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7+5i)-(-6+4i)= 7+5i +6-4i =\color{red}{7+6}\color{blue}{+5i -4i}=\color{red}{13}\color{blue}{+i}\)
2. \((-10-10i)+(8-8i)= -10-10i +8-8i =\color{red}{-10+8}\color{blue}{-10i -8i}=\color{red}{-2}\color{blue}{-18i}\)
3. \((-2-5i)-(5-3i)= -2-5i -5+3i =\color{red}{-2-5}\color{blue}{-5i +3i}=\color{red}{-7}\color{blue}{-2i}\)
4. \((3-5i)+(8-6i)= 3-5i +8-6i =\color{red}{3+8}\color{blue}{-5i -6i}=\color{red}{11}\color{blue}{-11i}\)
5. \(\frac{2+3i}{-7-10i}= \frac{2+3i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{-14+20i -21 i+30i^2 }{(-7)^2-(-10i)^2} = \frac{-14+20i -21 i-30}{49 + 100} = \frac{-44-i }{149} = \frac{-44}{149} + \frac{-1}{149}i \)
6. \((-2+8i)\cdot (+8i)= -16 i+64i^2 = \color{red}{-64}\color{blue}{-16i}\)
7. \((8+9i) \cdot (8+4i)= 64+32i +72 i+36i^2 = 64+32i +72 i-36= \color{red}{64-36}\color{blue}{+32i +72i}=\color{red}{28}\color{blue}{+104i}\)
8. \((10-7i) \cdot (7-6i)= 70-60i -49 i+42i^2 = 70-60i -49 i-42= \color{red}{70-42}\color{blue}{-60i -49i}=\color{red}{28}\color{blue}{-109i}\)
9. \((7-2i) \cdot (-2-8i)= -14-56i +4 i+16i^2 = -14-56i +4 i-16= \color{red}{-14-16}\color{blue}{-56i +4i}=\color{red}{-30}\color{blue}{-52i}\)
10. \(\frac{-5-7i}{7+9i}= \frac{-5-7i}{7+9i} \cdot \frac{7-9i}{7-9i} = \frac{-35+45i -49 i+63i^2 }{(7)^2-(9i)^2} = \frac{-35+45i -49 i-63}{49 + 81} = \frac{-98-4i }{130} = \frac{-49}{65} + \frac{-2}{65}i \)
11. \(\frac{-7-3i}{-6+10i}= \frac{-7-3i}{-6+10i} \cdot \frac{-6-10i}{-6-10i} = \frac{42+70i +18 i+30i^2 }{(-6)^2-(10i)^2} = \frac{42+70i +18 i-30}{36 + 100} = \frac{12+88i }{136} = \frac{3}{34} - \frac{-11}{17}i \)
12. \((-4+10i)-(-3+i)= -4+10i +3-i =\color{red}{-4+3}\color{blue}{+10i -i}=\color{red}{-1}\color{blue}{+9i}\)