Whakaoti i te (4+3i)(1-2i)/(4-3i)(1+2i)

$$\frac { ( 4 + 3 i ) ( 1 - 2 i ) } { ( 4 - 3 i ) ( 1 + 2 i ) }$$

Aromātai

$$\frac{3}{5}-\frac{4}{5}i=0.6-0.8i$$

Ngā Upane Otinga

Me whakarea ngā tau matatini 4+3i me 1-2i pēnā i te whakarea huarua.

$$\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)i^{2}}{\left(4-3i\right)\left(1+2i\right)}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right)}{\left(4-3i\right)\left(1+2i\right)}$$

Mahia ngā whakarea i roto o 4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right).

$$\frac{4-8i+3i+6}{\left(4-3i\right)\left(1+2i\right)}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 4-8i+3i+6.

$$\frac{4+6+\left(-8+3\right)i}{\left(4-3i\right)\left(1+2i\right)}$$

Mahia ngā tāpiri i roto o 4+6+\left(-8+3\right)i.

$$\frac{10-5i}{\left(4-3i\right)\left(1+2i\right)}$$

Me whakarea ngā tau matatini 4-3i me 1+2i pēnā i te whakarea huarua.

$$\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2i^{2}}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right)}$$

Mahia ngā whakarea i roto o 4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right).

$$\frac{10-5i}{4+8i-3i+6}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 4+8i-3i+6.

$$\frac{10-5i}{4+6+\left(8-3\right)i}$$

Mahia ngā tāpiri i roto o 4+6+\left(8-3\right)i.

$$\frac{10-5i}{10+5i}$$

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 10-5i.

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

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}.

$$\frac{\left(10-5i\right)\left(10-5i\right)}{10^{2}-5^{2}i^{2}}$$

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

$$\frac{\left(10-5i\right)\left(10-5i\right)}{125}$$

Me whakarea ngā tau matatini 10-5i me 10-5i pēnā i te whakarea huarua.

$$\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)i^{2}}{125}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right)}{125}$$

Mahia ngā whakarea i roto o 10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right).

$$\frac{100-50i-50i-25}{125}$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 100-50i-50i-25.

$$\frac{100-25+\left(-50-50\right)i}{125}$$

Mahia ngā tāpiri i roto o 100-25+\left(-50-50\right)i.

$$\frac{75-100i}{125}$$

Whakawehea te 75-100i ki te 125, kia riro ko \frac{3}{5}-\frac{4}{5}i.

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

Wāhi Tūturu

$$\frac{3}{5} = 0.6$$

Ngā Upane Otinga

Me whakarea ngā tau matatini 4+3i me 1-2i pēnā i te whakarea huarua.

$$Re(\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)i^{2}}{\left(4-3i\right)\left(1+2i\right)})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right)}{\left(4-3i\right)\left(1+2i\right)})$$

Mahia ngā whakarea i roto o 4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right).

$$Re(\frac{4-8i+3i+6}{\left(4-3i\right)\left(1+2i\right)})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 4-8i+3i+6.

$$Re(\frac{4+6+\left(-8+3\right)i}{\left(4-3i\right)\left(1+2i\right)})$$

Mahia ngā tāpiri i roto o 4+6+\left(-8+3\right)i.

$$Re(\frac{10-5i}{\left(4-3i\right)\left(1+2i\right)})$$

Me whakarea ngā tau matatini 4-3i me 1+2i pēnā i te whakarea huarua.

$$Re(\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2i^{2}})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right)})$$

Mahia ngā whakarea i roto o 4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right).

$$Re(\frac{10-5i}{4+8i-3i+6})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 4+8i-3i+6.

$$Re(\frac{10-5i}{4+6+\left(8-3\right)i})$$

Mahia ngā tāpiri i roto o 4+6+\left(8-3\right)i.

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

Me whakarea te taurunga me te tauraro o \frac{10-5i}{10+5i} ki te haumi hiato o te tauraro, 10-5i.

$$Re(\frac{\left(10-5i\right)\left(10-5i\right)}{\left(10+5i\right)\left(10-5i\right)})$$

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}.

$$Re(\frac{\left(10-5i\right)\left(10-5i\right)}{10^{2}-5^{2}i^{2}})$$

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

$$Re(\frac{\left(10-5i\right)\left(10-5i\right)}{125})$$

Me whakarea ngā tau matatini 10-5i me 10-5i pēnā i te whakarea huarua.

$$Re(\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)i^{2}}{125})$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$Re(\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right)}{125})$$

Mahia ngā whakarea i roto o 10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right).

$$Re(\frac{100-50i-50i-25}{125})$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 100-50i-50i-25.

$$Re(\frac{100-25+\left(-50-50\right)i}{125})$$

Mahia ngā tāpiri i roto o 100-25+\left(-50-50\right)i.

$$Re(\frac{75-100i}{125})$$

Whakawehea te 75-100i ki te 125, kia riro ko \frac{3}{5}-\frac{4}{5}i.

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

Ko te wāhi tūturu o \frac{3}{5}-\frac{4}{5}i ko \frac{3}{5}.

$$\frac{3}{5}$$