Whakaoti i te -1-4i/-5-9i

$$\frac { - 1 - 4 i } { - 5 - 9 i }$$

Aromātai

$$\frac{41}{106}+\frac{11}{106}i\approx 0.386792453+0.103773585i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, -5+9i.

$$\frac{\left(-1-4i\right)\left(-5+9i\right)}{\left(-5-9i\right)\left(-5+9i\right)}$$

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}.

$$\frac{\left(-1-4i\right)\left(-5+9i\right)}{\left(-5\right)^{2}-9^{2}i^{2}}$$

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

$$\frac{\left(-1-4i\right)\left(-5+9i\right)}{106}$$

Me whakarea ngā tau matatini -1-4i me -5+9i pēnā i te whakarea huarua.

$$\frac{-\left(-5\right)-9i-4i\left(-5\right)-4\times 9i^{2}}{106}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{-\left(-5\right)-9i-4i\left(-5\right)-4\times 9\left(-1\right)}{106}$$

Mahia ngā whakarea i roto o -\left(-5\right)-9i-4i\left(-5\right)-4\times 9\left(-1\right).

$$\frac{5-9i+20i+36}{106}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 5-9i+20i+36.

$$\frac{5+36+\left(-9+20\right)i}{106}$$

Mahia ngā tāpiri i roto o 5+36+\left(-9+20\right)i.

$$\frac{41+11i}{106}$$

Whakawehea te 41+11i ki te 106, kia riro ko \frac{41}{106}+\frac{11}{106}i.

$$\frac{41}{106}+\frac{11}{106}i$$

Wāhi Tūturu

$$\frac{41}{106} = 0.3867924528301887$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{-1-4i}{-5-9i} ki te haumi hiato o te tauraro, -5+9i.

$$Re(\frac{\left(-1-4i\right)\left(-5+9i\right)}{\left(-5-9i\right)\left(-5+9i\right)})$$

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}.

$$Re(\frac{\left(-1-4i\right)\left(-5+9i\right)}{\left(-5\right)^{2}-9^{2}i^{2}})$$

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

$$Re(\frac{\left(-1-4i\right)\left(-5+9i\right)}{106})$$

Me whakarea ngā tau matatini -1-4i me -5+9i pēnā i te whakarea huarua.

$$Re(\frac{-\left(-5\right)-9i-4i\left(-5\right)-4\times 9i^{2}}{106})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{-\left(-5\right)-9i-4i\left(-5\right)-4\times 9\left(-1\right)}{106})$$

Mahia ngā whakarea i roto o -\left(-5\right)-9i-4i\left(-5\right)-4\times 9\left(-1\right).

$$Re(\frac{5-9i+20i+36}{106})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 5-9i+20i+36.

$$Re(\frac{5+36+\left(-9+20\right)i}{106})$$

Mahia ngā tāpiri i roto o 5+36+\left(-9+20\right)i.

$$Re(\frac{41+11i}{106})$$

Whakawehea te 41+11i ki te 106, kia riro ko \frac{41}{106}+\frac{11}{106}i.

$$Re(\frac{41}{106}+\frac{11}{106}i)$$

Ko te wāhi tūturu o \frac{41}{106}+\frac{11}{106}i ko \frac{41}{106}.

$$\frac{41}{106}$$