Het complexe vlak

Antwoorden bij de opgaven

1. 1. `5text(i)`
   2. `x=-5text(i) vv x=5text(i)`
   3. `x=2+2text(i) vv x=2-2text(i)`
   4. `x=-1 vv x=-3`
   5. `x=-2+text(i)sqrt(26) vv x=-2-text(i)sqrt(26)`
2. 1. -
   2. op de `x`-as
3. Zie de Theorie
4. 1. `z_1 + z_2 = 4-text(i)`
   2. `z_1-z_2=-2-3text(i)`
   3. -
5. 1. -
   2. `z_1*z_2=5-5text(i)`
   3. `text(Re)(z_1*z_2)=5` en `text(Im)(z_1*z_2)=-5`
6. 1. -
   2. `z_1/z_2=0,1-0,7text(i)`
   3. `text(Re)(z_1/z_2)=0,1` en `text(Im)(z_1/z_2)=-0,7
7. `-16+16text(i)`
8. -
9. 1. `5-2text(i)`
   2. `6+6text(i)`
   3. 1
   4. `14-2text(i)`
   5. `-2+2text(i)`
   6. `-0,08+0,56text(i)`
10. -
11. 1. De vector bij `3text(i)` is even lang als bij 3, maar precies `1/2 pi` om `O` gedraaid.
    2. Ja, hetzelfde verband.
    3. Inderdaad: bij `text(i)z` en `z` horen even lange vectoren, maar de vector bij `text(i)z` is met `1/2 pi` om `O` gedraaid t.o.v. de vector bij `z`.
    4. `text(i)` en `text(i)^2=-1` voldoen ook aan dit verband
12. 1. `text(Re)(z)=-3` en `text(Im)(z)=-1`
    2. `text(Re)(z)=8` en `text(Im)(z)=-1`
    3. `text(Re)(z)=62` en `text(Im)(z)=-63`
    4. `text(Re)(z)=25` en `text(Im)(z)=0`
    5. `text(Re)(z)=9` en `text(Im)(z)=0`
    6. `text(Re)(z)=21/34` en `text(Im)(z)=1/34`
13. 1. `z=2+text(i)sqrt(8)` V `z=2-text(i)sqrt(8)`
    2. `z=3text(i)` V `z=-text(i)`
    3. `z=text(i)sqrt(8)` V `z=-text(i)sqrt(8)`
    4. `z=1+2text(i)`
    5. `z=2/34 + 26/34 text(i)`
14. `text(Re)((2-3i)^5)=122` en `text(Im)((2-3text(i))^5)=597`
15. -
16. 1. `z_1+z_2=1+3text(i)`, `z_1-z_2=-7+5text(i)`
    2. `5+2text(i)`
    3. `-8+19text(i)`
    4. `- 16/17 + 13/17 text(i)`
17. 1. `text(Re)(z)=5` en `text(Im)(z)=3`
    2. `text(Re)(z)=3/34` en `text(Im)(z)=5/34`
    3. `text(Re)(z)=69` en `text(Im)(z)=21`
    4. `text(Re)(z)=-0,5` en `text(Im)(z)=1/2 sqrt(3)`