Whakaoti i te (2+3i)div(1+2i)

$$( 2 + 3 i ) \div ( 1 + 2 i )$$

Aromātai

$$\frac{8}{5}-\frac{1}{5}i=1.6-0.2i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 1-2i.

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

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}.

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

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

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

Me whakarea ngā tau matatini 2+3i me 1-2i pēnā i te whakarea huarua.

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

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$\frac{2-4i+3i+6}{5}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 2-4i+3i+6.

$$\frac{2+6+\left(-4+3\right)i}{5}$$

Mahia ngā tāpiri i roto o 2+6+\left(-4+3\right)i.

$$\frac{8-i}{5}$$

Whakawehea te 8-i ki te 5, kia riro ko \frac{8}{5}-\frac{1}{5}i.

$$\frac{8}{5}-\frac{1}{5}i$$

Wāhi Tūturu

$$\frac{8}{5} = 1\frac{3}{5} = 1.6$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{2+3i}{1+2i} ki te haumi hiato o te tauraro, 1-2i.

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

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}.

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

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

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

Me whakarea ngā tau matatini 2+3i me 1-2i pēnā i te whakarea huarua.

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

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$Re(\frac{2-4i+3i+6}{5})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 2-4i+3i+6.

$$Re(\frac{2+6+\left(-4+3\right)i}{5})$$

Mahia ngā tāpiri i roto o 2+6+\left(-4+3\right)i.

$$Re(\frac{8-i}{5})$$

Whakawehea te 8-i ki te 5, kia riro ko \frac{8}{5}-\frac{1}{5}i.

$$Re(\frac{8}{5}-\frac{1}{5}i)$$

Ko te wāhi tūturu o \frac{8}{5}-\frac{1}{5}i ko \frac{8}{5}.

$$\frac{8}{5}$$