Datrys z=-5+10z/3+4i

$$z = \frac { - 5 + 10 z } { 3 + 4 i }$$

Datrys ar gyfer z

$$z=\frac{7}{13}+\frac{4}{13}i\approx 0.538461538+0.307692308i$$

Camau ar gyfer Datrys Hafaliad Llinol

Rhannu pob term -5+10z â 3+4i i gael \frac{-5}{3+4i}+\frac{10z}{3+4i}.

$$z=\frac{-5}{3+4i}+\frac{10z}{3+4i}$$

Lluoswch rifiadur ac enwadur \frac{-5}{3+4i} gyda chyfiau cymhleth yr enwadur 3-4i.

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

Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Drwy ddiffiniad, i^{2} yw -1. Cyfrifwch yr enwadur.

$$z=\frac{-5\left(3-4i\right)}{25}+\frac{10z}{3+4i}$$

Lluoswch -5 â 3-4i.

$$z=\frac{-5\times 3-5\times \left(-4i\right)}{25}+\frac{10z}{3+4i}$$

Gwnewch y gwaith lluosi yn -5\times 3-5\times \left(-4i\right).

$$z=\frac{-15+20i}{25}+\frac{10z}{3+4i}$$

Rhannu -15+20i â 25 i gael -\frac{3}{5}+\frac{4}{5}i.

$$z=-\frac{3}{5}+\frac{4}{5}i+\frac{10z}{3+4i}$$

Rhannu 10z â 3+4i i gael \left(\frac{6}{5}-\frac{8}{5}i\right)z.

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

Tynnu \left(\frac{6}{5}-\frac{8}{5}i\right)z o'r ddwy ochr.

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

Cyfuno z a \left(-\frac{6}{5}+\frac{8}{5}i\right)z i gael \left(-\frac{1}{5}+\frac{8}{5}i\right)z.

$$\left(-\frac{1}{5}+\frac{8}{5}i\right)z=-\frac{3}{5}+\frac{4}{5}i$$

Rhannu’r ddwy ochr â -\frac{1}{5}+\frac{8}{5}i.

$$z=\frac{-\frac{3}{5}+\frac{4}{5}i}{-\frac{1}{5}+\frac{8}{5}i}$$

Lluoswch rifiadur ac enwadur \frac{-\frac{3}{5}+\frac{4}{5}i}{-\frac{1}{5}+\frac{8}{5}i} gyda chyfiau cymhleth yr enwadur -\frac{1}{5}-\frac{8}{5}i.

$$z=\frac{\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{1}{5}-\frac{8}{5}i\right)}{\left(-\frac{1}{5}+\frac{8}{5}i\right)\left(-\frac{1}{5}-\frac{8}{5}i\right)}$$

Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$z=\frac{\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{1}{5}-\frac{8}{5}i\right)}{\left(-\frac{1}{5}\right)^{2}-\left(\frac{8}{5}\right)^{2}i^{2}}$$

Drwy ddiffiniad, i^{2} yw -1. Cyfrifwch yr enwadur.

$$z=\frac{\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{1}{5}-\frac{8}{5}i\right)}{\frac{13}{5}}$$

Lluoswch y rhifau cymhleth -\frac{3}{5}+\frac{4}{5}i a -\frac{1}{5}-\frac{8}{5}i yn yr un modd ag y byddech yn lluosogi binomialau.

$$z=\frac{-\frac{3}{5}\left(-\frac{1}{5}\right)-\frac{3}{5}\times \left(-\frac{8}{5}i\right)+\frac{4}{5}i\left(-\frac{1}{5}\right)+\frac{4}{5}\left(-\frac{8}{5}\right)i^{2}}{\frac{13}{5}}$$

Drwy ddiffiniad, i^{2} yw -1.

$$z=\frac{-\frac{3}{5}\left(-\frac{1}{5}\right)-\frac{3}{5}\times \left(-\frac{8}{5}i\right)+\frac{4}{5}i\left(-\frac{1}{5}\right)+\frac{4}{5}\left(-\frac{8}{5}\right)\left(-1\right)}{\frac{13}{5}}$$

Gwnewch y gwaith lluosi yn -\frac{3}{5}\left(-\frac{1}{5}\right)-\frac{3}{5}\times \left(-\frac{8}{5}i\right)+\frac{4}{5}i\left(-\frac{1}{5}\right)+\frac{4}{5}\left(-\frac{8}{5}\right)\left(-1\right).

$$z=\frac{\frac{3}{25}+\frac{24}{25}i-\frac{4}{25}i+\frac{32}{25}}{\frac{13}{5}}$$

Cyfunwch y rhannau real a dychmygus yn \frac{3}{25}+\frac{24}{25}i-\frac{4}{25}i+\frac{32}{25}.

$$z=\frac{\frac{3}{25}+\frac{32}{25}+\left(\frac{24}{25}-\frac{4}{25}\right)i}{\frac{13}{5}}$$

Gwnewch y gwaith adio yn \frac{3}{25}+\frac{32}{25}+\left(\frac{24}{25}-\frac{4}{25}\right)i.

$$z=\frac{\frac{7}{5}+\frac{4}{5}i}{\frac{13}{5}}$$

Rhannu \frac{7}{5}+\frac{4}{5}i â \frac{13}{5} i gael \frac{7}{13}+\frac{4}{13}i.

$$z=\frac{7}{13}+\frac{4}{13}i$$