(2-3i)(x+yi)=4+i eching

$$( 2 - 3 i ) ( x + y i ) = 4 + i$$

x uchun yechish

$$x=\frac{5}{13}+\frac{14}{13}i-iy$$

Yechim qadamlari

Ikki tarafini 2-3i ga bo‘ling.

$$x+yi=\frac{4+i}{2-3i}$$

\frac{4+i}{2-3i}ning surat va maxrajini murakkab tutash maxraj 2+3i bilan ko‘paytiring.

$$x+yi=\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}$$

\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)} ichidagi ko‘paytirishlarni bajaring.

$$x+yi=\frac{5+14i}{13}$$

\frac{5}{13}+\frac{14}{13}i ni olish uchun 5+14i ni 13 ga bo‘ling.

$$x+yi=\frac{5}{13}+\frac{14}{13}i$$

Ikkala tarafdan yi ni ayirish.

$$x=\frac{5}{13}+\frac{14}{13}i-yi$$

-i hosil qilish uchun -1 va i ni ko'paytirish.

$$x=\frac{5}{13}+\frac{14}{13}i-iy$$

y uchun yechish

$$y=ix+\left(\frac{14}{13}-\frac{5}{13}i\right)$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikki tarafini 2-3i ga bo‘ling.

$$x+yi=\frac{4+i}{2-3i}$$

\frac{4+i}{2-3i}ning surat va maxrajini murakkab tutash maxraj 2+3i bilan ko‘paytiring.

$$x+yi=\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)}$$

\frac{\left(4+i\right)\left(2+3i\right)}{\left(2-3i\right)\left(2+3i\right)} ichidagi ko‘paytirishlarni bajaring.

$$x+yi=\frac{5+14i}{13}$$

\frac{5}{13}+\frac{14}{13}i ni olish uchun 5+14i ni 13 ga bo‘ling.

$$x+yi=\frac{5}{13}+\frac{14}{13}i$$

Ikkala tarafdan x ni ayirish.

$$yi=\frac{5}{13}+\frac{14}{13}i-x$$

Tenglama standart shaklda.

$$iy=\frac{5}{13}+\frac{14}{13}i-x$$

Ikki tarafini i ga bo‘ling.

$$\frac{iy}{i}=\frac{\frac{5}{13}+\frac{14}{13}i-x}{i}$$

i ga bo'lish i ga ko'paytirishni bekor qiladi.

$$y=\frac{\frac{5}{13}+\frac{14}{13}i-x}{i}$$

\frac{5}{13}+\frac{14}{13}i-x ni i ga bo'lish.

$$y=ix+\left(\frac{14}{13}-\frac{5}{13}i\right)$$