(6+2i)-(1+3i)/(-1+i)-2 eching

$$\frac { ( 6 + 2 i ) - ( 1 + 3 i ) } { ( - 1 + i ) - 2 }$$

Baholash

$$-\frac{8}{5}-\frac{1}{5}i=-1,6-0,2i$$

Yechim qadamlari

1+3i ni 6+2i dan mos real va mavhum qismlarni ayirish orqali ayiring.

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

6 dan 1 ni ayirish. 2 dan 3 ni ayirish.

$$\frac{5-i}{-1+i-2}$$

2 ni -1+i dan mos real va mavhum qismlarni ayirish orqali ayiring.

$$\frac{5-i}{-1-2+i}$$

-3 olish uchun -1 dan 2 ni ayirish.

$$\frac{5-i}{-3+i}$$

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, -3-i.

$$\frac{\left(5-i\right)\left(-3-i\right)}{\left(-3+i\right)\left(-3-i\right)}$$

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

$$\frac{\left(5-i\right)\left(-3-i\right)}{\left(-3\right)^{2}-i^{2}}$$

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

$$\frac{\left(5-i\right)\left(-3-i\right)}{10}$$

Binomlarni ko‘paytirgandek 5-i va -3-i murakkab sonlarni ko‘paytiring.

$$\frac{5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-i^{2}\right)}{10}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-\left(-1\right)\right)}{10}$$

5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-\left(-1\right)\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-15-5i+3i-1}{10}$$

-15-5i+3i-1 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-15-1+\left(-5+3\right)i}{10}$$

-15-1+\left(-5+3\right)i ichida qo‘shishlarni bajaring.

$$\frac{-16-2i}{10}$$

-\frac{8}{5}-\frac{1}{5}i ni olish uchun -16-2i ni 10 ga bo‘ling.

$$-\frac{8}{5}-\frac{1}{5}i$$

Ashyoviy qism

$$-\frac{8}{5} = -1\frac{3}{5} = -1,6$$

Yechim qadamlari

1+3i ni 6+2i dan mos real va mavhum qismlarni ayirish orqali ayiring.

$$Re(\frac{6-1+\left(2-3\right)i}{-1+i-2})$$

6 dan 1 ni ayirish. 2 dan 3 ni ayirish.

$$Re(\frac{5-i}{-1+i-2})$$

2 ni -1+i dan mos real va mavhum qismlarni ayirish orqali ayiring.

$$Re(\frac{5-i}{-1-2+i})$$

-3 olish uchun -1 dan 2 ni ayirish.

$$Re(\frac{5-i}{-3+i})$$

\frac{5-i}{-3+i}ning surat va maxrajini murakkab tutash maxraj -3-i bilan ko‘paytiring.

$$Re(\frac{\left(5-i\right)\left(-3-i\right)}{\left(-3+i\right)\left(-3-i\right)})$$

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

$$Re(\frac{\left(5-i\right)\left(-3-i\right)}{\left(-3\right)^{2}-i^{2}})$$

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

$$Re(\frac{\left(5-i\right)\left(-3-i\right)}{10})$$

Binomlarni ko‘paytirgandek 5-i va -3-i murakkab sonlarni ko‘paytiring.

$$Re(\frac{5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-i^{2}\right)}{10})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-\left(-1\right)\right)}{10})$$

5\left(-3\right)+5\left(-i\right)-i\left(-3\right)-\left(-\left(-1\right)\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-15-5i+3i-1}{10})$$

-15-5i+3i-1 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-15-1+\left(-5+3\right)i}{10})$$

-15-1+\left(-5+3\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-16-2i}{10})$$

-\frac{8}{5}-\frac{1}{5}i ni olish uchun -16-2i ni 10 ga bo‘ling.

$$Re(-\frac{8}{5}-\frac{1}{5}i)$$

-\frac{8}{5}-\frac{1}{5}i ning real qismi – -\frac{8}{5}.

$$-\frac{8}{5}$$