Whakaoti i te -1+19/2i/8-3i

$$\frac{ -1+ \frac{ 19 }{ 2 } i }{ 8-3i }$$

Aromātai

$$-\frac{1}{2}+i=-0.5+i$$

Ngā Upane Otinga

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 8+3i.

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{\left(8-3i\right)\left(8+3i\right)}$$

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}.

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{8^{2}-3^{2}i^{2}}$$

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

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{73}$$

Me whakarea ngā tau matatini -1+\frac{19}{2}i me 8+3i pēnā i te whakarea huarua.

$$\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3i^{2}}{73}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right)}{73}$$

Mahia ngā whakarea i roto o -8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right).

$$\frac{-8-3i+76i-\frac{57}{2}}{73}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -8-3i+76i-\frac{57}{2}.

$$\frac{-8-\frac{57}{2}+\left(-3+76\right)i}{73}$$

Mahia ngā tāpiri i roto o -8-\frac{57}{2}+\left(-3+76\right)i.

$$\frac{-\frac{73}{2}+73i}{73}$$

Whakawehea te -\frac{73}{2}+73i ki te 73, kia riro ko -\frac{1}{2}+i.

$$-\frac{1}{2}+i$$

Wāhi Tūturu

$$-\frac{1}{2} = -0.5$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{-1+\frac{19}{2}i}{8-3i} ki te haumi hiato o te tauraro, 8+3i.

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{\left(8-3i\right)\left(8+3i\right)})$$

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}.

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{8^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{73})$$

Me whakarea ngā tau matatini -1+\frac{19}{2}i me 8+3i pēnā i te whakarea huarua.

$$Re(\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3i^{2}}{73})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right)}{73})$$

Mahia ngā whakarea i roto o -8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right).

$$Re(\frac{-8-3i+76i-\frac{57}{2}}{73})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki -8-3i+76i-\frac{57}{2}.

$$Re(\frac{-8-\frac{57}{2}+\left(-3+76\right)i}{73})$$

Mahia ngā tāpiri i roto o -8-\frac{57}{2}+\left(-3+76\right)i.

$$Re(\frac{-\frac{73}{2}+73i}{73})$$

Whakawehea te -\frac{73}{2}+73i ki te 73, kia riro ko -\frac{1}{2}+i.

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

Ko te wāhi tūturu o -\frac{1}{2}+i ko -\frac{1}{2}.

$$-\frac{1}{2}$$