Whakaoti i te (2+3i)x+(5+4i)y=49-11i

$$( 2 + 3 i ) x + ( 5 + 4 i ) y = 49 - 11 i$$

Whakaoti mō x

$$x=\left(-\frac{22}{13}+\frac{7}{13}i\right)y+\left(5-13i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \left(5+4i\right)y mai i ngā taha e rua.

$$\left(2+3i\right)x=49-11i-\left(5+4i\right)y$$

Whakareatia te -1 ki te 5+4i, ka -5-4i.

$$\left(2+3i\right)x=49-11i+\left(-5-4i\right)y$$

He hanga arowhānui tō te whārite.

$$\left(2+3i\right)x=\left(-5-4i\right)y+\left(49-11i\right)$$

Whakawehea ngā taha e rua ki te 2+3i.

$$\frac{\left(2+3i\right)x}{2+3i}=\frac{\left(-5-4i\right)y+\left(49-11i\right)}{2+3i}$$

Mā te whakawehe ki te 2+3i ka wetekia te whakareanga ki te 2+3i.

$$x=\frac{\left(-5-4i\right)y+\left(49-11i\right)}{2+3i}$$

Whakawehe 49-11i+\left(-5-4i\right)y ki te 2+3i.

$$x=\left(-\frac{22}{13}+\frac{7}{13}i\right)y+\left(5-13i\right)$$

Whakaoti mō y

$$y=\left(-\frac{22}{41}-\frac{7}{41}i\right)x+\left(\frac{201}{41}-\frac{251}{41}i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \left(2+3i\right)x mai i ngā taha e rua.

$$\left(5+4i\right)y=49-11i-\left(2+3i\right)x$$

Whakareatia te -1 ki te 2+3i, ka -2-3i.

$$\left(5+4i\right)y=49-11i+\left(-2-3i\right)x$$

He hanga arowhānui tō te whārite.

$$\left(5+4i\right)y=\left(-2-3i\right)x+\left(49-11i\right)$$

Whakawehea ngā taha e rua ki te 5+4i.

$$\frac{\left(5+4i\right)y}{5+4i}=\frac{\left(-2-3i\right)x+\left(49-11i\right)}{5+4i}$$

Mā te whakawehe ki te 5+4i ka wetekia te whakareanga ki te 5+4i.

$$y=\frac{\left(-2-3i\right)x+\left(49-11i\right)}{5+4i}$$

Whakawehe 49-11i+\left(-2-3i\right)x ki te 5+4i.

$$y=\left(-\frac{22}{41}-\frac{7}{41}i\right)x+\left(\frac{201}{41}-\frac{251}{41}i\right)$$