8+6i/55+10i eching

$$\frac { 8 + 6 i } { 55 + 10 i }$$

Baholash

$$\frac{4}{25}+\frac{2}{25}i=0,16+0,08i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 55-10i.

$$\frac{\left(8+6i\right)\left(55-10i\right)}{\left(55+10i\right)\left(55-10i\right)}$$

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

$$\frac{\left(8+6i\right)\left(55-10i\right)}{55^{2}-10^{2}i^{2}}$$

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

$$\frac{\left(8+6i\right)\left(55-10i\right)}{3125}$$

Binomlarni ko‘paytirgandek 8+6i va 55-10i murakkab sonlarni ko‘paytiring.

$$\frac{8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)i^{2}}{3125}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)\left(-1\right)}{3125}$$

8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{440-80i+330i+60}{3125}$$

440-80i+330i+60 ichida real va mavhum qismlarni birlashtiring.

$$\frac{440+60+\left(-80+330\right)i}{3125}$$

440+60+\left(-80+330\right)i ichida qo‘shishlarni bajaring.

$$\frac{500+250i}{3125}$$

\frac{4}{25}+\frac{2}{25}i ni olish uchun 500+250i ni 3125 ga bo‘ling.

$$\frac{4}{25}+\frac{2}{25}i$$

Ashyoviy qism

$$\frac{4}{25} = 0,16$$

Yechim qadamlari

\frac{8+6i}{55+10i}ning surat va maxrajini murakkab tutash maxraj 55-10i bilan ko‘paytiring.

$$Re(\frac{\left(8+6i\right)\left(55-10i\right)}{\left(55+10i\right)\left(55-10i\right)})$$

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

$$Re(\frac{\left(8+6i\right)\left(55-10i\right)}{55^{2}-10^{2}i^{2}})$$

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

$$Re(\frac{\left(8+6i\right)\left(55-10i\right)}{3125})$$

Binomlarni ko‘paytirgandek 8+6i va 55-10i murakkab sonlarni ko‘paytiring.

$$Re(\frac{8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)i^{2}}{3125})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)\left(-1\right)}{3125})$$

8\times 55+8\times \left(-10i\right)+6i\times 55+6\left(-10\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{440-80i+330i+60}{3125})$$

440-80i+330i+60 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{440+60+\left(-80+330\right)i}{3125})$$

440+60+\left(-80+330\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{500+250i}{3125})$$

\frac{4}{25}+\frac{2}{25}i ni olish uchun 500+250i ni 3125 ga bo‘ling.

$$Re(\frac{4}{25}+\frac{2}{25}i)$$

\frac{4}{25}+\frac{2}{25}i ning real qismi – \frac{4}{25}.

$$\frac{4}{25}$$