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

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

Aromātai

$$-\frac{2}{41}-\frac{23}{41}i\approx -0.048780488-0.56097561i$$

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.

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

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$\frac{-2-23i}{41}$$

Whakawehea te -2-23i ki te 41, kia riro ko -\frac{2}{41}-\frac{23}{41}i.

$$-\frac{2}{41}-\frac{23}{41}i$$

Wāhi Tūturu

$$-\frac{2}{41} = -0.04878048780487805$$

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.

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

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$Re(\frac{-2-23i}{41})$$

Whakawehea te -2-23i ki te 41, kia riro ko -\frac{2}{41}-\frac{23}{41}i.

$$Re(-\frac{2}{41}-\frac{23}{41}i)$$

Ko te wāhi tūturu o -\frac{2}{41}-\frac{23}{41}i ko -\frac{2}{41}.

$$-\frac{2}{41}$$