Whakaoti i te z/z-8=-1-2i

$$\frac { z } { z - 8 } = - 1 - 2 i$$

Whakaoti mō z

$$z=6+2i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe z ki 8 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te z-8.

$$z=\left(-1-2i\right)\left(z-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -1-2i ki te z-8.

$$z=\left(-1-2i\right)z+\left(8+16i\right)$$

Tangohia te \left(-1-2i\right)z mai i ngā taha e rua.

$$z-\left(-1-2i\right)z=8+16i$$

Pahekotia te z me \left(1+2i\right)z, ka \left(2+2i\right)z.

$$\left(2+2i\right)z=8+16i$$

Whakawehea ngā taha e rua ki te 2+2i.

$$z=\frac{8+16i}{2+2i}$$

Me whakarea te taurunga me te tauraro o \frac{8+16i}{2+2i} ki te haumi hiato o te tauraro, 2-2i.

$$z=\frac{\left(8+16i\right)\left(2-2i\right)}{\left(2+2i\right)\left(2-2i\right)}$$

Mahia ngā whakarea i roto o \frac{\left(8+16i\right)\left(2-2i\right)}{\left(2+2i\right)\left(2-2i\right)}.

$$z=\frac{48+16i}{8}$$

Whakawehea te 48+16i ki te 8, kia riro ko 6+2i.

$$z=6+2i$$