Whakaoti i te 1-4i/3+i

$$\frac { 1 - 4 i } { 3 + i }$$

Aromātai

$$-\frac{1}{10}-\frac{13}{10}i=-0.1-1.3i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 3-i.

$$\frac{\left(1-4i\right)\left(3-i\right)}{\left(3+i\right)\left(3-i\right)}$$

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}.

$$\frac{\left(1-4i\right)\left(3-i\right)}{3^{2}-i^{2}}$$

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

$$\frac{\left(1-4i\right)\left(3-i\right)}{10}$$

Me whakarea ngā tau matatini 1-4i me 3-i pēnā i te whakarea huarua.

$$\frac{1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)i^{2}}{10}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)\left(-1\right)}{10}$$

Mahia ngā whakarea i roto o 1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)\left(-1\right).

$$\frac{3-i-12i-4}{10}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 3-i-12i-4.

$$\frac{3-4+\left(-1-12\right)i}{10}$$

Mahia ngā tāpiri i roto o 3-4+\left(-1-12\right)i.

$$\frac{-1-13i}{10}$$

Whakawehea te -1-13i ki te 10, kia riro ko -\frac{1}{10}-\frac{13}{10}i.

$$-\frac{1}{10}-\frac{13}{10}i$$

Wāhi Tūturu

$$-\frac{1}{10} = -0.1$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{1-4i}{3+i} ki te haumi hiato o te tauraro, 3-i.

$$Re(\frac{\left(1-4i\right)\left(3-i\right)}{\left(3+i\right)\left(3-i\right)})$$

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}.

$$Re(\frac{\left(1-4i\right)\left(3-i\right)}{3^{2}-i^{2}})$$

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

$$Re(\frac{\left(1-4i\right)\left(3-i\right)}{10})$$

Me whakarea ngā tau matatini 1-4i me 3-i pēnā i te whakarea huarua.

$$Re(\frac{1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)i^{2}}{10})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)\left(-1\right)}{10})$$

Mahia ngā whakarea i roto o 1\times 3+1\left(-i\right)-4i\times 3-4\left(-1\right)\left(-1\right).

$$Re(\frac{3-i-12i-4}{10})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 3-i-12i-4.

$$Re(\frac{3-4+\left(-1-12\right)i}{10})$$

Mahia ngā tāpiri i roto o 3-4+\left(-1-12\right)i.

$$Re(\frac{-1-13i}{10})$$

Whakawehea te -1-13i ki te 10, kia riro ko -\frac{1}{10}-\frac{13}{10}i.

$$Re(-\frac{1}{10}-\frac{13}{10}i)$$

Ko te wāhi tūturu o -\frac{1}{10}-\frac{13}{10}i ko -\frac{1}{10}.

$$-\frac{1}{10}$$