2-i/3+i eching

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

Baholash

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

Yechim qadamlari

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

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

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

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

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

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

Binomlarni ko‘paytirgandek 2-i va 3-i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{2\times 3+2\left(-i\right)-i\times 3-\left(-\left(-1\right)\right)}{10}$$

2\times 3+2\left(-i\right)-i\times 3-\left(-\left(-1\right)\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{6-2i-3i-1}{10}$$

6-2i-3i-1 ichida real va mavhum qismlarni birlashtiring.

$$\frac{6-1+\left(-2-3\right)i}{10}$$

6-1+\left(-2-3\right)i ichida qo‘shishlarni bajaring.

$$\frac{5-5i}{10}$$

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

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

Ashyoviy qism

$$\frac{1}{2} = 0,5$$

Yechim qadamlari

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

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

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

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

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

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

Binomlarni ko‘paytirgandek 2-i va 3-i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{2\times 3+2\left(-i\right)-i\times 3-\left(-\left(-1\right)\right)}{10})$$

2\times 3+2\left(-i\right)-i\times 3-\left(-\left(-1\right)\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{6-2i-3i-1}{10})$$

6-2i-3i-1 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{6-1+\left(-2-3\right)i}{10})$$

6-1+\left(-2-3\right)i ichida qo‘shishlarni bajaring.

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

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

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

\frac{1}{2}-\frac{1}{2}i ning real qismi – \frac{1}{2}.

$$\frac{1}{2}$$