3-1/(2-i)(5+2i) eching

$$\frac { 3 - 1 } { ( 2 - i ) ( 5 + 2 i ) }$$

Baholash

$$\frac{24}{145}+\frac{2}{145}i\approx 0,165517241+0,013793103i$$

Yechim qadamlari

2 olish uchun 3 dan 1 ni ayirish.

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

Binomlarni ko‘paytirgandek 2-i va 5+2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{2}{2\times 5+2\times \left(2i\right)-i\times 5-2\left(-1\right)}$$

2\times 5+2\times \left(2i\right)-i\times 5-2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2}{10+4i-5i+2}$$

10+4i-5i+2 ichida real va mavhum qismlarni birlashtiring.

$$\frac{2}{10+2+\left(4-5\right)i}$$

10+2+\left(4-5\right)i ichida qo‘shishlarni bajaring.

$$\frac{2}{12-i}$$

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 12+i.

$$\frac{2\left(12+i\right)}{\left(12-i\right)\left(12+i\right)}$$

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

$$\frac{2\left(12+i\right)}{12^{2}-i^{2}}$$

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

$$\frac{2\left(12+i\right)}{145}$$

2 ni 12+i marotabaga ko'paytirish.

$$\frac{2\times 12+2i}{145}$$

2\times 12+2i ichidagi ko‘paytirishlarni bajaring.

$$\frac{24+2i}{145}$$

\frac{24}{145}+\frac{2}{145}i ni olish uchun 24+2i ni 145 ga bo‘ling.

$$\frac{24}{145}+\frac{2}{145}i$$

Ashyoviy qism

$$\frac{24}{145} = 0,16551724137931034$$

Yechim qadamlari

2 olish uchun 3 dan 1 ni ayirish.

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

Binomlarni ko‘paytirgandek 2-i va 5+2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

2\times 5+2\times \left(2i\right)-i\times 5-2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{2}{10+4i-5i+2})$$

10+4i-5i+2 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{2}{10+2+\left(4-5\right)i})$$

10+2+\left(4-5\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{2}{12-i})$$

\frac{2}{12-i}ning surat va maxrajini murakkab tutash maxraj 12+i bilan ko‘paytiring.

$$Re(\frac{2\left(12+i\right)}{\left(12-i\right)\left(12+i\right)})$$

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

$$Re(\frac{2\left(12+i\right)}{12^{2}-i^{2}})$$

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

$$Re(\frac{2\left(12+i\right)}{145})$$

2 ni 12+i marotabaga ko'paytirish.

$$Re(\frac{2\times 12+2i}{145})$$

2\times 12+2i ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{24+2i}{145})$$

\frac{24}{145}+\frac{2}{145}i ni olish uchun 24+2i ni 145 ga bo‘ling.

$$Re(\frac{24}{145}+\frac{2}{145}i)$$

\frac{24}{145}+\frac{2}{145}i ning real qismi – \frac{24}{145}.

$$\frac{24}{145}$$