Whakaoti i te 2-3i/5-4i

$$\frac { 2 - 3 i } { 5 - 4 i }$$

Aromātai

$$\frac{22}{41}-\frac{7}{41}i\approx 0.536585366-0.170731707i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 5+4i.

$$\frac{\left(2-3i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)}$$

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}.

$$\frac{\left(2-3i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}}$$

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

$$\frac{\left(2-3i\right)\left(5+4i\right)}{41}$$

Me whakarea ngā tau matatini 2-3i me 5+4i pēnā i te whakarea huarua.

$$\frac{2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4i^{2}}{41}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4\left(-1\right)}{41}$$

Mahia ngā whakarea i roto o 2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4\left(-1\right).

$$\frac{10+8i-15i+12}{41}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 10+8i-15i+12.

$$\frac{10+12+\left(8-15\right)i}{41}$$

Mahia ngā tāpiri i roto o 10+12+\left(8-15\right)i.

$$\frac{22-7i}{41}$$

Whakawehea te 22-7i ki te 41, kia riro ko \frac{22}{41}-\frac{7}{41}i.

$$\frac{22}{41}-\frac{7}{41}i$$

Wāhi Tūturu

$$\frac{22}{41} = 0.5365853658536586$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{2-3i}{5-4i} ki te haumi hiato o te tauraro, 5+4i.

$$Re(\frac{\left(2-3i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)})$$

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}.

$$Re(\frac{\left(2-3i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}})$$

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

$$Re(\frac{\left(2-3i\right)\left(5+4i\right)}{41})$$

Me whakarea ngā tau matatini 2-3i me 5+4i pēnā i te whakarea huarua.

$$Re(\frac{2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4i^{2}}{41})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4\left(-1\right)}{41})$$

Mahia ngā whakarea i roto o 2\times 5+2\times \left(4i\right)-3i\times 5-3\times 4\left(-1\right).

$$Re(\frac{10+8i-15i+12}{41})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 10+8i-15i+12.

$$Re(\frac{10+12+\left(8-15\right)i}{41})$$

Mahia ngā tāpiri i roto o 10+12+\left(8-15\right)i.

$$Re(\frac{22-7i}{41})$$

Whakawehea te 22-7i ki te 41, kia riro ko \frac{22}{41}-\frac{7}{41}i.

$$Re(\frac{22}{41}-\frac{7}{41}i)$$

Ko te wāhi tūturu o \frac{22}{41}-\frac{7}{41}i ko \frac{22}{41}.

$$\frac{22}{41}$$