Whakaoti i te 6+15iz-7i=0

$$6 + 15 i z - 7 i = 0$$

Whakaoti mō z

$$z=\frac{7}{15}+\frac{2}{5}i\approx 0.466666667+0.4i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 6 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$15iz-7i=-6$$

Me tāpiri te 7i ki ngā taha e rua.

$$15iz=-6+7i$$

Whakawehea ngā taha e rua ki te 15i.

$$z=\frac{-6+7i}{15i}$$

Me whakarea tahi te taurunga me te tauraro o \frac{-6+7i}{15i} ki te wae pohewa i.

$$z=\frac{\left(-6+7i\right)i}{15i^{2}}$$

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

$$z=\frac{\left(-6+7i\right)i}{-15}$$

Whakareatia -6+7i ki te i.

$$z=\frac{-6i+7i^{2}}{-15}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$z=\frac{-6i+7\left(-1\right)}{-15}$$

Mahia ngā whakarea i roto o -6i+7\left(-1\right). Whakaraupapatia anō ngā kīanga tau.

$$z=\frac{-7-6i}{-15}$$

Whakawehea te -7-6i ki te -15, kia riro ko \frac{7}{15}+\frac{2}{5}i.

$$z=\frac{7}{15}+\frac{2}{5}i$$