Whakaoti i te frac{left(5+10texttt{i}right)20}{5+10texttt{i}+20}

$$\frac{ \left( 5+10 \texttt{i} \right) 20 }{ 5+10 \texttt{i} +20 }$$

Aromātai

$$\frac{180}{29}+\frac{160}{29}i\approx 6.206896552+5.517241379i$$

Ngā Upane Otinga

Whakareatia 5+10i ki te 20.

$$\frac{5\times 20+10i\times 20}{5+10i+20}$$

Mahia ngā whakarea i roto o 5\times 20+10i\times 20.

$$\frac{100+200i}{5+10i+20}$$

Whakakotahitia ngā tau tūturu me ngā tau pōhewa i roto o 5+10i me te 20.

$$\frac{100+200i}{5+20+10i}$$

Tāpiri 5 ki te 20.

$$\frac{100+200i}{25+10i}$$

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 25-10i.

$$\frac{\left(100+200i\right)\left(25-10i\right)}{\left(25+10i\right)\left(25-10i\right)}$$

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}.

$$\frac{\left(100+200i\right)\left(25-10i\right)}{25^{2}-10^{2}i^{2}}$$

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

$$\frac{\left(100+200i\right)\left(25-10i\right)}{725}$$

Me whakarea ngā tau matatini 100+200i me 25-10i pēnā i te whakarea huarua.

$$\frac{100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)i^{2}}{725}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)\left(-1\right)}{725}$$

Mahia ngā whakarea i roto o 100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)\left(-1\right).

$$\frac{2500-1000i+5000i+2000}{725}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 2500-1000i+5000i+2000.

$$\frac{2500+2000+\left(-1000+5000\right)i}{725}$$

Mahia ngā tāpiri i roto o 2500+2000+\left(-1000+5000\right)i.

$$\frac{4500+4000i}{725}$$

Whakawehea te 4500+4000i ki te 725, kia riro ko \frac{180}{29}+\frac{160}{29}i.

$$\frac{180}{29}+\frac{160}{29}i$$

Wāhi Tūturu

$$\frac{180}{29} = 6\frac{6}{29} = 6.206896551724138$$

Ngā Upane Otinga

Whakareatia 5+10i ki te 20.

$$Re(\frac{5\times 20+10i\times 20}{5+10i+20})$$

Mahia ngā whakarea i roto o 5\times 20+10i\times 20.

$$Re(\frac{100+200i}{5+10i+20})$$

Whakakotahitia ngā tau tūturu me ngā tau pōhewa i roto o 5+10i me te 20.

$$Re(\frac{100+200i}{5+20+10i})$$

Tāpiri 5 ki te 20.

$$Re(\frac{100+200i}{25+10i})$$

Me whakarea te taurunga me te tauraro o \frac{100+200i}{25+10i} ki te haumi hiato o te tauraro, 25-10i.

$$Re(\frac{\left(100+200i\right)\left(25-10i\right)}{\left(25+10i\right)\left(25-10i\right)})$$

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}.

$$Re(\frac{\left(100+200i\right)\left(25-10i\right)}{25^{2}-10^{2}i^{2}})$$

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

$$Re(\frac{\left(100+200i\right)\left(25-10i\right)}{725})$$

Me whakarea ngā tau matatini 100+200i me 25-10i pēnā i te whakarea huarua.

$$Re(\frac{100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)i^{2}}{725})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)\left(-1\right)}{725})$$

Mahia ngā whakarea i roto o 100\times 25+100\times \left(-10i\right)+200i\times 25+200\left(-10\right)\left(-1\right).

$$Re(\frac{2500-1000i+5000i+2000}{725})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 2500-1000i+5000i+2000.

$$Re(\frac{2500+2000+\left(-1000+5000\right)i}{725})$$

Mahia ngā tāpiri i roto o 2500+2000+\left(-1000+5000\right)i.

$$Re(\frac{4500+4000i}{725})$$

Whakawehea te 4500+4000i ki te 725, kia riro ko \frac{180}{29}+\frac{160}{29}i.

$$Re(\frac{180}{29}+\frac{160}{29}i)$$

Ko te wāhi tūturu o \frac{180}{29}+\frac{160}{29}i ko \frac{180}{29}.

$$\frac{180}{29}$$