Whakaoti i te (2x+i)(4+3i)=(5+yi)

$$( 2 x + i ) ( 4 + 3 i ) = ( 5 + y i )$$

Whakaoti mō x

$$x=\left(\frac{3}{50}+\frac{2}{25}i\right)y+\left(\frac{2}{5}-\frac{4}{5}i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+i ki te 4+3i.

$$\left(8+6i\right)x+\left(-3+4i\right)=5+yi$$

Tangohia te -3+4i mai i ngā taha e rua.

$$\left(8+6i\right)x=5+yi-\left(-3+4i\right)$$

Whakareatia te -1 ki te -3+4i, ka 3-4i.

$$\left(8+6i\right)x=5+yi+\left(3-4i\right)$$

Mahia ngā tāpiri i roto o 5+\left(3-4i\right).

$$\left(8+6i\right)x=yi+8-4i$$

He hanga arowhānui tō te whārite.

$$\left(8+6i\right)x=iy+\left(8-4i\right)$$

Whakawehea ngā taha e rua ki te 8+6i.

$$\frac{\left(8+6i\right)x}{8+6i}=\frac{iy+\left(8-4i\right)}{8+6i}$$

Mā te whakawehe ki te 8+6i ka wetekia te whakareanga ki te 8+6i.

$$x=\frac{iy+\left(8-4i\right)}{8+6i}$$

Whakawehe iy+\left(8-4i\right) ki te 8+6i.

$$x=\left(\frac{3}{50}+\frac{2}{25}i\right)y+\left(\frac{2}{5}-\frac{4}{5}i\right)$$

Whakaoti mō y

$$y=\left(6-8i\right)x+\left(4+8i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+i ki te 4+3i.

$$\left(8+6i\right)x+\left(-3+4i\right)=5+yi$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5+yi=\left(8+6i\right)x+\left(-3+4i\right)$$

Tangohia te 5 mai i ngā taha e rua.

$$yi=\left(8+6i\right)x+\left(-3+4i\right)-5$$

Mahia ngā tāpiri i roto o -3+4i-5.

$$yi=\left(8+6i\right)x-8+4i$$

He hanga arowhānui tō te whārite.

$$iy=\left(8+6i\right)x+\left(-8+4i\right)$$

Whakawehea ngā taha e rua ki te i.

$$\frac{iy}{i}=\frac{\left(8+6i\right)x+\left(-8+4i\right)}{i}$$

Mā te whakawehe ki te i ka wetekia te whakareanga ki te i.

$$y=\frac{\left(8+6i\right)x+\left(-8+4i\right)}{i}$$

Whakawehe \left(8+6i\right)x+\left(-8+4i\right) ki te i.

$$y=\left(6-8i\right)x+\left(4+8i\right)$$