Whakaoti i te 2-2z(1+i)=4i-2

$$2 - 2 z ( 1 + i ) = 4 i - 2$$

Whakaoti mō z

$$z=-2i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia 2 ki te 1+i.

$$2-\left(2\times 1+2i\right)z=4i-2$$

Mahia ngā whakarea i roto o 2\times 1+2i.

$$2-\left(2+2i\right)z=4i-2$$

Whakareatia te -1 ki te 2+2i, ka -2-2i.

$$2+\left(-2-2i\right)z=4i-2$$

Tangohia te 2 mai i ngā taha e rua.

$$\left(-2-2i\right)z=4i-2-2$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 4i-2-2.

$$\left(-2-2i\right)z=-2-2+4i$$

Tāpiri -2 ki te -2.

$$\left(-2-2i\right)z=-4+4i$$

Whakawehea ngā taha e rua ki te -2-2i.

$$z=\frac{-4+4i}{-2-2i}$$

Me whakarea te taurunga me te tauraro o \frac{-4+4i}{-2-2i} ki te haumi hiato o te tauraro, -2+2i.

$$z=\frac{\left(-4+4i\right)\left(-2+2i\right)}{\left(-2-2i\right)\left(-2+2i\right)}$$

Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$z=\frac{\left(-4+4i\right)\left(-2+2i\right)}{\left(-2\right)^{2}-2^{2}i^{2}}$$

Hei tōna tikanga, ko te i^{2} ko -1. Tātaitia te tauraro.

$$z=\frac{\left(-4+4i\right)\left(-2+2i\right)}{8}$$

Me whakarea ngā tau matatini -4+4i me -2+2i pēnā i te whakarea huarua.

$$z=\frac{-4\left(-2\right)-4\times \left(2i\right)+4i\left(-2\right)+4\times 2i^{2}}{8}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$z=\frac{-4\left(-2\right)-4\times \left(2i\right)+4i\left(-2\right)+4\times 2\left(-1\right)}{8}$$

Mahia ngā whakarea i roto o -4\left(-2\right)-4\times \left(2i\right)+4i\left(-2\right)+4\times 2\left(-1\right).

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

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 8-8i-8i-8.

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

Mahia ngā tāpiri i roto o 8-8+\left(-8-8\right)i.

$$z=\frac{-16i}{8}$$

Whakawehea te -16i ki te 8, kia riro ko -2i.

$$z=-2i$$