$z=1$ V $z=\mathrm{-0,5}+\mathrm{0,5}i\sqrt{3}$ V $z=\mathrm{-0,5}-\mathrm{0,5}i\sqrt{3}$

$z=\mathrm{0,5}\sqrt{2}+\mathrm{0,5}\text{i}\sqrt{2}$ `vv` $z=\mathrm{0,5}\sqrt{2}-\mathrm{0,5}\text{i}\sqrt{2}$ `vv` $z=\mathrm{-0,5}\sqrt{2}+\mathrm{0,5}\text{i}\sqrt{2}$ `vv` $z=\mathrm{-0,5}\sqrt{2}-\mathrm{0,5}i\sqrt{2}$

Omdat `text(-)1 = text(i)^2` .

Doen.

$z=\mathrm{-2,5}\pm \mathrm{0,5}i\sqrt{\left(15\right)}$

Doen.

$z_1=-1+\mathrm{0,5}\sqrt{2}+(1+\mathrm{0,5}\sqrt{2}\text{i};z_2=-1cos\left(\frac{7}{12}\pi \right)+(1+sin\left(\frac{7}{12}\pi \right))\text{i};z_3=-1+cos\left(\frac{11}{12}\pi \right)+(1+sin\left(\frac{11}{12}\pi \right))\text{i};$
$z_4=-1-\mathrm{0,5}\sqrt{2}+(1-\mathrm{0,5}\sqrt{2})\text{i};z_5=-1+cos\left(\frac{19}{12}\pi \right)+(1+sin\left(\frac{19}{12}\pi \right))\text{i};z_6=-1+cos\left(\frac{23}{12}\pi \right)+(1+sin\left(\frac{23}{12}\pi \right))\text{i}$

Doen.

$z=\frac{7}{13}-\frac{22}{13}\text{i}$

$z=1+2\text{i}$

$z=\mathrm{-1,5}\text{i}$

$z_1=\mathrm{0,5}\sqrt{3}+\mathrm{0,5}\text{i};z_2=\mathrm{-0,5}\sqrt{3}+\mathrm{0,5}\text{i};z_3=-\text{i}$

`z_1=sqrt(2)+text(i)sqrt(2); z_2=text(-)sqrt(2)+text(i)sqrt(2); z_3=text(-)sqrt(2)-text(i)sqrt(2); z_4=sqrt(2)-text(i)sqrt(2)`

$z_1=-\mathrm{0,5}\sqrt{2}+\mathrm{0,5}\text{i}\sqrt{2};z_2=\mathrm{0,5}\sqrt{2}-\mathrm{0,5}\text{i}\sqrt{2}$

$z_1=3\text{i};z_2=\mathrm{-1,5}\sqrt{3}-\mathrm{1,5}\text{i};z_3=\mathrm{1,5}\sqrt{3}-\mathrm{1,5}\text{i}$

$z_1=\sqrt{3}+\text{i};z_2=-2+\text{i}\sqrt{3};z_3=\mathrm{-}\sqrt{3}-\text{i};z_4=2-\text{i}\sqrt{3}$

$z_1=\mathrm{0,25}\sqrt{2}-\mathrm{0,25}\text{i}\sqrt{2};z_2=-\mathrm{0,25}\sqrt{2}+\mathrm{0,25}\text{i}\sqrt{2}$

$z_1=1+\text{i};z_2=2\text{i};z_3=-1;z_4=0$

$z_1=\mathrm{-}\frac{1}{6}+\frac{1}{6}\text{i}\sqrt{\left(35\right)};z_2=\mathrm{-}\frac{1}{6}-\frac{1}{6}\text{i}\sqrt{\left(35\right)}$

$z_1=3+\text{i};z_2=-3-\text{i}$

$z_1\approx \mathrm{0,36}+\mathrm{1,72}\text{i};z_2\approx \mathrm{-1,54}+\mathrm{3,49}\text{i};z_3\approx \mathrm{-2,02}+\mathrm{0,78}\text{i}$

$z_1=-1+\mathrm{0,5}\text{i}\sqrt{2};z_2=-1-\mathrm{0,5}\text{i}\sqrt{2}$

Eerst schrijven als $z^4=-16$ `vv` $z^4=1$ etc.

$z=\mathrm{3,2}-\mathrm{2,4}\text{i}$

$z_1=1+\sqrt{2}+\text{i}\sqrt{2};z_2=1-\sqrt{2}-\text{i}\sqrt{2}$

$z_1=\mathrm{0,5}+\mathrm{0,5}\text{i}\sqrt{3};z_2=\text{i}\sqrt{3};z_3=-\mathrm{0,5}+\mathrm{0,5}\text{i}\sqrt{3};z_4=-\mathrm{0,5}-\mathrm{0,5}\text{i}\sqrt{3};z_5=-\text{i}\sqrt{3};z_6=\mathrm{0,5}-\mathrm{0,5}\text{i}\sqrt{3}$

$z=0$

Doen.

$x=2$

$x^3+6x-20=(x-2)(x^2+2x+10)=0$ geeft $x=2$ V $x=-1\pm 3i$

$x=-4$ `vv` $x=\mathrm{-0,5}\pm \mathrm{0,5}\text{i}\sqrt{3}$

$x=\frac{1}{3}$ `vv` $x=-2\pm \text{i}\sqrt{2}$

$z=0$ `vv` $z=\pm \mathrm{0,5}\sqrt{\left(3\right)}+\mathrm{1,5}\text{i}$

$z=\mathrm{0,4}+\mathrm{0,2}\text{i}$ `vv` $z=\mathrm{-0,4}-\mathrm{0,2}\text{i}$

$z_1\approx \mathrm{1,93}+\mathrm{0,52}\text{i};z_2\approx \mathrm{0,52}+\mathrm{1,93}\text{i};z_3\approx \mathrm{-1,41}+\mathrm{1,41}\text{i};z_4\approx \mathrm{-1,93}-\mathrm{0,52}\text{i};z_5\approx \mathrm{-0,52}-\mathrm{1,93}\text{i};z_6\approx \mathrm{1,41}-\mathrm{1,41}\text{i}$

$z_1\approx \mathrm{-0,62}-\mathrm{3,12}\text{i};z_2\approx \mathrm{0,12}+\mathrm{0,62}\text{i}$