Whakaoti i te |5-i/1+i|

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

Aromātai

$$\sqrt{13}\approx 3.605551275$$

Ngā Upane Otinga

Me whakarea te taurunga me te tauraro o \frac{5-i}{1+i} ki te haumi hiato o te tauraro, 1-i.

$$|\frac{\left(5-i\right)\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}|$$

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}.

$$|\frac{\left(5-i\right)\left(1-i\right)}{1^{2}-i^{2}}|$$

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

$$|\frac{\left(5-i\right)\left(1-i\right)}{2}|$$

Me whakarea ngā tau matatini 5-i me 1-i pēnā i te whakarea huarua.

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

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$|\frac{5-5i-i-1}{2}|$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 5-5i-i-1.

$$|\frac{5-1+\left(-5-1\right)i}{2}|$$

Mahia ngā tāpiri i roto o 5-1+\left(-5-1\right)i.

$$|\frac{4-6i}{2}|$$

Whakawehea te 4-6i ki te 2, kia riro ko 2-3i.

$$|2-3i|$$

Ko te tau tōpū o tētahi tau matatini a+bi ko \sqrt{a^{2}+b^{2}}. Ko te tau tōpū o 2-3i ko \sqrt{13}.

$$\sqrt{13}$$

Wāhi Tūturu

$$\sqrt{13} = 3.605551275$$