Whakaoti i te z=1+3i/2-i(i)

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

Whakaoti mō z

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$z=\frac{\left(1+3i\right)\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}i$$

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}.

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

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

$$z=\frac{\left(1+3i\right)\left(2+i\right)}{5}i$$

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

$$z=\frac{1\times 2+i+3i\times 2+3i^{2}}{5}i$$

Hei tōna tikanga, ko te i^{2} ko -1.

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

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

$$z=\frac{2+i+6i-3}{5}i$$

Whakakotahitia ngā wāhi tūturu me ngā wāhi pōhewa ki 2+i+6i-3.

$$z=\frac{2-3+\left(1+6\right)i}{5}i$$

Mahia ngā tāpiri i roto o 2-3+\left(1+6\right)i.

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

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

$$z=\left(-\frac{1}{5}+\frac{7}{5}i\right)i$$

Whakareatia -\frac{1}{5}+\frac{7}{5}i ki te i.

$$z=-\frac{1}{5}i+\frac{7}{5}i^{2}$$

Hei tōna tikanga, ko te i^{2} ko -1.

$$z=-\frac{1}{5}i+\frac{7}{5}\left(-1\right)$$

Mahia ngā whakarea i roto o -\frac{1}{5}i+\frac{7}{5}\left(-1\right). Whakaraupapatia anō ngā kīanga tau.

$$z=-\frac{7}{5}-\frac{1}{5}i$$

Tautapa z

$$z≔-\frac{7}{5}-\frac{1}{5}i$$