Datrys 3+xi/1+2i=y+2i

$$\frac { 3 + x i } { 1 + 2 i } = y + 2 i$$

Datrys ar gyfer ξ

$$\xi =\left(1+2i\right)y+\left(-7+2i\right)$$

Camau ar gyfer Datrys Hafaliad Llinol

Rhannu pob term 3+\xi â 1+2i i gael \frac{3}{1+2i}+\frac{\xi }{1+2i}.

$$\frac{3}{1+2i}+\frac{\xi }{1+2i}=y+2i$$

Lluoswch rifiadur ac enwadur \frac{3}{1+2i} gyda chyfiau cymhleth yr enwadur 1-2i.

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

Gwnewch y gwaith lluosi yn \frac{3\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}.

$$\frac{3-6i}{5}+\frac{\xi }{1+2i}=y+2i$$

Rhannu 3-6i â 5 i gael \frac{3}{5}-\frac{6}{5}i.

$$\frac{3}{5}-\frac{6}{5}i+\frac{\xi }{1+2i}=y+2i$$

Tynnu \frac{3}{5}-\frac{6}{5}i o'r ddwy ochr.

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

Lluosi -1 a \frac{3}{5}-\frac{6}{5}i i gael -\frac{3}{5}+\frac{6}{5}i.

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

Gwnewch y gwaith adio yn 2i+\left(-\frac{3}{5}+\frac{6}{5}i\right).

$$\frac{\xi }{1+2i}=y-\frac{3}{5}+\frac{16}{5}i$$

Mae'r hafaliad yn y ffurf safonol.

$$\left(\frac{1}{5}-\frac{2}{5}i\right)\xi =y+\left(-\frac{3}{5}+\frac{16}{5}i\right)$$

Rhannu’r ddwy ochr â \frac{1}{5}-\frac{2}{5}i.

$$\frac{\left(\frac{1}{5}-\frac{2}{5}i\right)\xi }{\frac{1}{5}-\frac{2}{5}i}=\frac{y+\left(-\frac{3}{5}+\frac{16}{5}i\right)}{\frac{1}{5}-\frac{2}{5}i}$$

Mae rhannu â \frac{1}{5}-\frac{2}{5}i yn dad-wneud lluosi â \frac{1}{5}-\frac{2}{5}i.

$$\xi =\frac{y+\left(-\frac{3}{5}+\frac{16}{5}i\right)}{\frac{1}{5}-\frac{2}{5}i}$$

Rhannwch y+\left(-\frac{3}{5}+\frac{16}{5}i\right) â \frac{1}{5}-\frac{2}{5}i.

$$\xi =\left(1+2i\right)y+\left(-7+2i\right)$$

Datrys ar gyfer y

$$y=\left(\frac{1}{5}-\frac{2}{5}i\right)\xi +\left(\frac{3}{5}-\frac{16}{5}i\right)$$