Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((4+4i)-(-10-2i)= 4+4i +10+2i =\color{red}{4+10}\color{blue}{+4i +2i}=\color{red}{14}\color{blue}{+6i}\)
2. \((10-7i) \cdot (10-3i)= 100-30i -70 i+21i^2 = 100-30i -70 i-21= \color{red}{100-21}\color{blue}{-30i -70i}=\color{red}{79}\color{blue}{-100i}\)
3. \(\frac{6-7i}{10+3i}= \frac{6-7i}{10+3i} \cdot \frac{10-3i}{10-3i} = \frac{60-18i -70 i+21i^2 }{(10)^2-(3i)^2} = \frac{60-18i -70 i-21}{100 + 9} = \frac{39-88i }{109} = \frac{39}{109} + \frac{-88}{109}i \)
4. \(\frac{7-i}{8-10i}= \frac{7-i}{8-10i} \cdot \frac{8+10i}{8+10i} = \frac{56+70i -8 i-10i^2 }{(8)^2-(-10i)^2} = \frac{56+70i -8 i+10}{64 + 100} = \frac{66+62i }{164} = \frac{33}{82} - \frac{-31}{82}i \)
5. \((5-9i)-(7-10i)= 5-9i -7+10i =\color{red}{5-7}\color{blue}{-9i +10i}=\color{red}{-2}\color{blue}{+i}\)
6. \((-7-7i)+(-8+6i)= -7-7i -8+6i =\color{red}{-7-8}\color{blue}{-7i +6i}=\color{red}{-15}\color{blue}{-i}\)
7. \(\frac{1+5i}{-4+i}= \frac{1+5i}{-4+i} \cdot \frac{-4-i}{-4-i} = \frac{-4-i -20 i-5i^2 }{(-4)^2-(1i)^2} = \frac{-4-i -20 i+5}{16 + 1} = \frac{1-21i }{17} = \frac{1}{17} + \frac{-21}{17}i \)
8. \(\frac{-9+2i}{4-5i}= \frac{-9+2i}{4-5i} \cdot \frac{4+5i}{4+5i} = \frac{-36-45i +8 i+10i^2 }{(4)^2-(-5i)^2} = \frac{-36-45i +8 i-10}{16 + 25} = \frac{-46-37i }{41} = \frac{-46}{41} + \frac{-37}{41}i \)
9. \((4-5i) \cdot (1-10i)= 4-40i -5 i+50i^2 = 4-40i -5 i-50= \color{red}{4-50}\color{blue}{-40i -5i}=\color{red}{-46}\color{blue}{-45i}\)
10. \((-2-6i)-(2-6i)= -2-6i -2+6i =\color{red}{-2-2}\color{blue}{-6i +6i}=\color{red}{-4}\)
11. \((-9i) \cdot (-4-9i)= +36 i+81i^2 = \color{red}{-81}\color{blue}{+36i}\)
12. \((9+9i)\cdot (-7i)= -63 i-63i^2 = \color{red}{63}\color{blue}{-63i}\)