Whakaoti i te -2-4i/5+9i

$$\frac { - 2 - 4 i } { 5 + 9 i }$$

Aromātai

$$-\frac{23}{53}-\frac{1}{53}i\approx -0.433962264-0.018867925i$$

Ngā Upane Otinga

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

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

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}.

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

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

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

Me whakarea ngā tau matatini -2-4i me 5-9i pēnā i te whakarea huarua.

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

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right)}{106}$$

Mahia ngā whakarea i roto o -2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right).

$$\frac{-10+18i-20i-36}{106}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -10+18i-20i-36.

$$\frac{-10-36+\left(18-20\right)i}{106}$$

Mahia ngā tāpiri i roto o -10-36+\left(18-20\right)i.

$$\frac{-46-2i}{106}$$

Whakawehea te -46-2i ki te 106, kia riro ko -\frac{23}{53}-\frac{1}{53}i.

$$-\frac{23}{53}-\frac{1}{53}i$$

Wāhi Tūturu

$$-\frac{23}{53} = -0.4339622641509434$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{-2-4i}{5+9i} ki te haumi hiato o te tauraro, 5-9i.

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

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}.

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

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

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

Me whakarea ngā tau matatini -2-4i me 5-9i pēnā i te whakarea huarua.

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

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right)}{106})$$

Mahia ngā whakarea i roto o -2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right).

$$Re(\frac{-10+18i-20i-36}{106})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -10+18i-20i-36.

$$Re(\frac{-10-36+\left(18-20\right)i}{106})$$

Mahia ngā tāpiri i roto o -10-36+\left(18-20\right)i.

$$Re(\frac{-46-2i}{106})$$

Whakawehea te -46-2i ki te 106, kia riro ko -\frac{23}{53}-\frac{1}{53}i.

$$Re(-\frac{23}{53}-\frac{1}{53}i)$$

Ko te wāhi tūturu o -\frac{23}{53}-\frac{1}{53}i ko -\frac{23}{53}.

$$-\frac{23}{53}$$