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.

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

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.

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

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.

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

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.

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

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}.

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