z=4-2i/1+i eching

$$z = \frac { 4 - 2 i } { 1 + i }$$

z uchun yechish

$$z=1-3i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{4-2i}{1+i}ning surat va maxrajini murakkab tutash maxraj 1-i bilan ko‘paytiring.

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

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

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

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

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

Binomlarni ko‘paytirgandek 4-2i va 1-i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

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

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

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

4-2+\left(-4-2\right)i ichida qo‘shishlarni bajaring.

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

1-3i ni olish uchun 2-6i ni 2 ga bo‘ling.

$$z=1-3i$$

z'ni tayinlash

$$z≔1-3i$$