2-2z(1+i)=4i-2 eching

$$2 - 2 z ( 1 + i ) = 4 i - 2$$

z uchun yechish

$$z=-2i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 ni 1+i marotabaga ko'paytirish.

$$2-\left(2\times 1+2i\right)z=4i-2$$

2\times 1+2i ichidagi ko‘paytirishlarni bajaring.

$$2-\left(2+2i\right)z=4i-2$$

-2-2i hosil qilish uchun -1 va 2+2i ni ko'paytirish.

$$2+\left(-2-2i\right)z=4i-2$$

Ikkala tarafdan 2 ni ayirish.

$$\left(-2-2i\right)z=4i-2-2$$

4i-2-2 ichida real va mavhum qismlarni birlashtiring.

$$\left(-2-2i\right)z=-2-2+4i$$

-2 ni -2 ga qo'shish.

$$\left(-2-2i\right)z=-4+4i$$

Ikki tarafini -2-2i ga bo‘ling.

$$z=\frac{-4+4i}{-2-2i}$$

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

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

Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ta’rifi bo‘yicha, i^{2} – bu -1. Maxrajini hisoblang.

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

Binomlarni ko‘paytirgandek -4+4i va -2+2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

-4\left(-2\right)-4\times \left(2i\right)+4i\left(-2\right)+4\times 2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$z=\frac{8-8i-8i-8}{8}$$

8-8i-8i-8 ichida real va mavhum qismlarni birlashtiring.

$$z=\frac{8-8+\left(-8-8\right)i}{8}$$

8-8+\left(-8-8\right)i ichida qo‘shishlarni bajaring.

$$z=\frac{-16i}{8}$$

-2i ni olish uchun -16i ni 8 ga bo‘ling.

$$z=-2i$$