Whakaoti i te 6i/7-3i

$$\frac { 6 i } { 7 - 3 i }$$

Aromātai

$$-\frac{9}{29}+\frac{21}{29}i\approx -0.310344828+0.724137931i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 7+3i.

$$\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)}$$

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}.

$$\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}}$$

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

$$\frac{6i\left(7+3i\right)}{58}$$

Whakareatia 6i ki te 7+3i.

$$\frac{6i\times 7+6\times 3i^{2}}{58}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{6i\times 7+6\times 3\left(-1\right)}{58}$$

Mahia ngā whakarea i roto o 6i\times 7+6\times 3\left(-1\right). Whakaraupapatia anō ngā kīanga tau.

$$\frac{-18+42i}{58}$$

Whakawehea te -18+42i ki te 58, kia riro ko -\frac{9}{29}+\frac{21}{29}i.

$$-\frac{9}{29}+\frac{21}{29}i$$

Wāhi Tūturu

$$-\frac{9}{29} = -0.3103448275862069$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{6i}{7-3i} ki te haumi hiato o te tauraro, 7+3i.

$$Re(\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)})$$

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}.

$$Re(\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{6i\left(7+3i\right)}{58})$$

Whakareatia 6i ki te 7+3i.

$$Re(\frac{6i\times 7+6\times 3i^{2}}{58})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{6i\times 7+6\times 3\left(-1\right)}{58})$$

Mahia ngā whakarea i roto o 6i\times 7+6\times 3\left(-1\right). Whakaraupapatia anō ngā kīanga tau.

$$Re(\frac{-18+42i}{58})$$

Whakawehea te -18+42i ki te 58, kia riro ko -\frac{9}{29}+\frac{21}{29}i.

$$Re(-\frac{9}{29}+\frac{21}{29}i)$$

Ko te wāhi tūturu o -\frac{9}{29}+\frac{21}{29}i ko -\frac{9}{29}.

$$-\frac{9}{29}$$