Réitigh 2/w=1+i/sqrt{3+i}

$$\frac { 2 } { w } = \frac { 1 + i } { \sqrt { 3 } + i }$$

Réitigh do w.

$$w=-\frac{8}{\sqrt{3}\left(-1-i\right)+\left(-1+i\right)}\approx 2.732050808-0.732050808i$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg w a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi w.

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

Méadaigh \frac{1}{4} faoi 1+i.

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

Déan iolrúcháin in \frac{1}{4}\times 1+\frac{1}{4}i.

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

Úsáid an t-airí dáileach chun \left(\frac{1}{4}+\frac{1}{4}i\right)w a mhéadú faoi 3^{\frac{1}{2}}-i.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Athordaigh na téarmaí.

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

Comhcheangail na téarmaí ar fad ina bhfuil w.

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

Roinn an dá thaobh faoi \left(\frac{1}{4}+\frac{1}{4}i\right)\sqrt{3}+\left(\frac{1}{4}-\frac{1}{4}i\right).

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

Má roinntear é faoi \left(\frac{1}{4}+\frac{1}{4}i\right)\sqrt{3}+\left(\frac{1}{4}-\frac{1}{4}i\right) cuirtear an iolrúchán faoi \left(\frac{1}{4}+\frac{1}{4}i\right)\sqrt{3}+\left(\frac{1}{4}-\frac{1}{4}i\right) ar ceal.

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

Roinn 2 faoi \left(\frac{1}{4}+\frac{1}{4}i\right)\sqrt{3}+\left(\frac{1}{4}-\frac{1}{4}i\right).

$$w=\frac{8}{\sqrt{3}\left(1+i\right)+\left(1-i\right)}$$