Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9-10i) \cdot (-5+5i)= -45+45i +50 i-50i^2 = -45+45i +50 i+50= \color{red}{-45+50}\color{blue}{+45i +50i}=\color{red}{5}\color{blue}{+95i}\)
2. \((9+9i)+(4-9i)= 9+9i +4-9i =\color{red}{9+4}\color{blue}{+9i -9i}=\color{red}{13}\)
3. \((-4+10i)-(-5-6i)= -4+10i +5+6i =\color{red}{-4+5}\color{blue}{+10i +6i}=\color{red}{1}\color{blue}{+16i}\)
4. \((8-3i)\cdot (-10i)= -80 i+30i^2 = \color{red}{-30}\color{blue}{-80i}\)
5. \((-10-3i)-(2+i)= -10-3i -2-i =\color{red}{-10-2}\color{blue}{-3i -i}=\color{red}{-12}\color{blue}{-4i}\)
6. \((-9+8i)+(8+6i)= -9+8i +8+6i =\color{red}{-9+8}\color{blue}{+8i +6i}=\color{red}{-1}\color{blue}{+14i}\)
7. \((-10i) \cdot (-8+6i)= +80 i-60i^2 = \color{red}{60}\color{blue}{+80i}\)
8. \((-7-2i)+(-1+5i)= -7-2i -1+5i =\color{red}{-7-1}\color{blue}{-2i +5i}=\color{red}{-8}\color{blue}{+3i}\)
9. \((1-6i)+(-8-6i)= 1-6i -8-6i =\color{red}{1-8}\color{blue}{-6i -6i}=\color{red}{-7}\color{blue}{-12i}\)
10. \((-7-6i) \cdot (-9+4i)= 63-28i +54 i-24i^2 = 63-28i +54 i+24= \color{red}{63+24}\color{blue}{-28i +54i}=\color{red}{87}\color{blue}{+26i}\)
11. \((2-7i) \cdot (-9-10i)= -18-20i +63 i+70i^2 = -18-20i +63 i-70= \color{red}{-18-70}\color{blue}{-20i +63i}=\color{red}{-88}\color{blue}{+43i}\)
12. \((-2-9i)-(-10-9i)= -2-9i +10+9i =\color{red}{-2+10}\color{blue}{-9i +9i}=\color{red}{8}\)