(1+i)z+5=2-3i eching

$$( 1 + i ) z + 5 = 2 - 3 i$$

z uchun yechish

$$z=-3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 5 ni ayirish.

$$\left(1+i\right)z=2-3i-5$$

5 ni 2-3i dan mos real va mavhum qismlarni ayirish orqali ayiring.

$$\left(1+i\right)z=2-5-3i$$

-3 olish uchun 2 dan 5 ni ayirish.

$$\left(1+i\right)z=-3-3i$$

Ikki tarafini 1+i ga bo‘ling.

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

\frac{-3-3i}{1+i}ning surat va maxrajini murakkab tutash maxraj 1-i bilan ko‘paytiring.

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

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

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

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

$$z=\frac{\left(-3-3i\right)\left(1-i\right)}{2}$$

Binomlarni ko‘paytirgandek -3-3i va 1-i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$z=\frac{-3-3\left(-i\right)-3i-3\left(-1\right)\left(-1\right)}{2}$$

-3-3\left(-i\right)-3i-3\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$z=\frac{-3+3i-3i-3}{2}$$

-3+3i-3i-3 ichida real va mavhum qismlarni birlashtiring.

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

-3-3+\left(3-3\right)i ichida qo‘shishlarni bajaring.

$$z=\frac{-6}{2}$$

-3 ni olish uchun -6 ni 2 ga bo‘ling.

$$z=-3$$