Whakaoti i te 5+5i/-3-4i

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

Aromātai

$$-\frac{7}{5}+\frac{1}{5}i=-1.4+0.2i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, -3+4i.

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

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}.

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

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

$$\frac{\left(5+5i\right)\left(-3+4i\right)}{25}$$

Me whakarea ngā tau matatini 5+5i me -3+4i pēnā i te whakarea huarua.

$$\frac{5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4i^{2}}{25}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4\left(-1\right)}{25}$$

Mahia ngā whakarea i roto o 5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4\left(-1\right).

$$\frac{-15+20i-15i-20}{25}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -15+20i-15i-20.

$$\frac{-15-20+\left(20-15\right)i}{25}$$

Mahia ngā tāpiri i roto o -15-20+\left(20-15\right)i.

$$\frac{-35+5i}{25}$$

Whakawehea te -35+5i ki te 25, kia riro ko -\frac{7}{5}+\frac{1}{5}i.

$$-\frac{7}{5}+\frac{1}{5}i$$

Wāhi Tūturu

$$-\frac{7}{5} = -1\frac{2}{5} = -1.4$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{5+5i}{-3-4i} ki te haumi hiato o te tauraro, -3+4i.

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

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}.

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

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

$$Re(\frac{\left(5+5i\right)\left(-3+4i\right)}{25})$$

Me whakarea ngā tau matatini 5+5i me -3+4i pēnā i te whakarea huarua.

$$Re(\frac{5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4i^{2}}{25})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4\left(-1\right)}{25})$$

Mahia ngā whakarea i roto o 5\left(-3\right)+5\times \left(4i\right)+5i\left(-3\right)+5\times 4\left(-1\right).

$$Re(\frac{-15+20i-15i-20}{25})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -15+20i-15i-20.

$$Re(\frac{-15-20+\left(20-15\right)i}{25})$$

Mahia ngā tāpiri i roto o -15-20+\left(20-15\right)i.

$$Re(\frac{-35+5i}{25})$$

Whakawehea te -35+5i ki te 25, kia riro ko -\frac{7}{5}+\frac{1}{5}i.

$$Re(-\frac{7}{5}+\frac{1}{5}i)$$

Ko te wāhi tūturu o -\frac{7}{5}+\frac{1}{5}i ko -\frac{7}{5}.

$$-\frac{7}{5}$$