left(-2+8iright)divleft(-2+6iright) eching

$$\left( -2+8i \right) \div \left( -2+6i \right)$$

Baholash

$$\frac{13}{10}-\frac{1}{10}i=1,3-0,1i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, -2-6i.

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

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

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

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

$$\frac{\left(-2+8i\right)\left(-2-6i\right)}{40}$$

Binomlarni ko‘paytirgandek -2+8i va -2-6i murakkab sonlarni ko‘paytiring.

$$\frac{-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)i^{2}}{40}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)\left(-1\right)}{40}$$

-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{4+12i-16i+48}{40}$$

4+12i-16i+48 ichida real va mavhum qismlarni birlashtiring.

$$\frac{4+48+\left(12-16\right)i}{40}$$

4+48+\left(12-16\right)i ichida qo‘shishlarni bajaring.

$$\frac{52-4i}{40}$$

\frac{13}{10}-\frac{1}{10}i ni olish uchun 52-4i ni 40 ga bo‘ling.

$$\frac{13}{10}-\frac{1}{10}i$$

Ashyoviy qism

$$\frac{13}{10} = 1\frac{3}{10} = 1,3$$

Yechim qadamlari

\frac{-2+8i}{-2+6i}ning surat va maxrajini murakkab tutash maxraj -2-6i bilan ko‘paytiring.

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

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

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

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

$$Re(\frac{\left(-2+8i\right)\left(-2-6i\right)}{40})$$

Binomlarni ko‘paytirgandek -2+8i va -2-6i murakkab sonlarni ko‘paytiring.

$$Re(\frac{-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)i^{2}}{40})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)\left(-1\right)}{40})$$

-2\left(-2\right)-2\times \left(-6i\right)+8i\left(-2\right)+8\left(-6\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{4+12i-16i+48}{40})$$

4+12i-16i+48 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{4+48+\left(12-16\right)i}{40})$$

4+48+\left(12-16\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{52-4i}{40})$$

\frac{13}{10}-\frac{1}{10}i ni olish uchun 52-4i ni 40 ga bo‘ling.

$$Re(\frac{13}{10}-\frac{1}{10}i)$$

\frac{13}{10}-\frac{1}{10}i ning real qismi – \frac{13}{10}.

$$\frac{13}{10}$$