Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \((-2+i) \cdot (7+6i)= -14-12i +7 i+6i^2 = -14-12i +7 i-6= \color{red}{-14-6}\color{blue}{-12i +7i}=\color{red}{-20}\color{blue}{-5i}\)
2. \((+7i) \cdot (2+2i)= +14 i+14i^2 = \color{red}{-14}\color{blue}{+14i}\)
3. \((3+8i)\cdot (+3i)= +9 i+24i^2 = \color{red}{-24}\color{blue}{+9i}\)
4. \((+8i) \cdot (-8-2i)= -64 i-16i^2 = \color{red}{16}\color{blue}{-64i}\)
5. \((5-2i) \cdot (2+10i)= 10+50i -4 i-20i^2 = 10+50i -4 i+20= \color{red}{10+20}\color{blue}{+50i -4i}=\color{red}{30}\color{blue}{+46i}\)
6. \((10-8i) \cdot (10-9i)= 100-90i -80 i+72i^2 = 100-90i -80 i-72= \color{red}{100-72}\color{blue}{-90i -80i}=\color{red}{28}\color{blue}{-170i}\)
7. \((+3i) \cdot (-5-4i)= -15 i-12i^2 = \color{red}{12}\color{blue}{-15i}\)
8. \((6+10i) \cdot (-6+8i)= -36+48i -60 i+80i^2 = -36+48i -60 i-80= \color{red}{-36-80}\color{blue}{+48i -60i}=\color{red}{-116}\color{blue}{-12i}\)
9. \((6-4i) \cdot (5+7i)= 30+42i -20 i-28i^2 = 30+42i -20 i+28= \color{red}{30+28}\color{blue}{+42i -20i}=\color{red}{58}\color{blue}{+22i}\)
10. \((10-7i)\cdot (-7i)= -70 i+49i^2 = \color{red}{-49}\color{blue}{-70i}\)
11. \((+10i) \cdot (9-i)= +90 i-10i^2 = \color{red}{10}\color{blue}{+90i}\)
12. \((+9i) \cdot (3+5i)= +27 i+45i^2 = \color{red}{-45}\color{blue}{+27i}\)