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

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

Whakaoti mō x

$$x=\frac{5}{13}+\frac{14}{13}i-iy$$

Ngā Upane Otinga

Whakawehea ngā taha e rua ki te 2-3i.

$$x+yi=\frac{4+i}{2-3i}$$

Me whakarea te taurunga me te tauraro o \frac{4+i}{2-3i} ki te haumi hiato o te tauraro, 2+3i.

$$x+yi=\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}$$

Mahia ngā whakarea i roto o \frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}.

$$x+yi=\frac{5+14i}{13}$$

Whakawehea te 5+14i ki te 13, kia riro ko \frac{5}{13}+\frac{14}{13}i.

$$x+yi=\frac{5}{13}+\frac{14}{13}i$$

Tangohia te yi mai i ngā taha e rua.

$$x=\frac{5}{13}+\frac{14}{13}i-yi$$

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

$$x=\frac{5}{13}+\frac{14}{13}i-iy$$

Whakaoti mō y

$$y=ix+\left(\frac{14}{13}-\frac{5}{13}i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawehea ngā taha e rua ki te 2-3i.

$$x+yi=\frac{4+i}{2-3i}$$

Me whakarea te taurunga me te tauraro o \frac{4+i}{2-3i} ki te haumi hiato o te tauraro, 2+3i.

$$x+yi=\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}$$

Mahia ngā whakarea i roto o \frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}.

$$x+yi=\frac{5+14i}{13}$$

Whakawehea te 5+14i ki te 13, kia riro ko \frac{5}{13}+\frac{14}{13}i.

$$x+yi=\frac{5}{13}+\frac{14}{13}i$$

Tangohia te x mai i ngā taha e rua.

$$yi=\frac{5}{13}+\frac{14}{13}i-x$$

He hanga arowhānui tō te whārite.

$$iy=\frac{5}{13}+\frac{14}{13}i-x$$

Whakawehea ngā taha e rua ki te i.

$$\frac{iy}{i}=\frac{\frac{5}{13}+\frac{14}{13}i-x}{i}$$

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

$$y=\frac{\frac{5}{13}+\frac{14}{13}i-x}{i}$$

Whakawehe \frac{5}{13}+\frac{14}{13}i-x ki te i.

$$y=ix+\left(\frac{14}{13}-\frac{5}{13}i\right)$$