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

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

Baholash

$$\frac{11}{10}+\frac{7}{10}i=1,1+0,7i$$

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}.

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

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.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

-2\times 2-2\times \left(-6i\right)+8i\times 2+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.

$$\frac{44+28i}{40}$$

\frac{11}{10}+\frac{7}{10}i ni olish uchun 44+28i ni 40 ga bo‘ling.

$$\frac{11}{10}+\frac{7}{10}i$$

Ashyoviy qism

$$\frac{11}{10} = 1\frac{1}{10} = 1,1$$

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}.

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

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.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

-2\times 2-2\times \left(-6i\right)+8i\times 2+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.

$$Re(\frac{44+28i}{40})$$

\frac{11}{10}+\frac{7}{10}i ni olish uchun 44+28i ni 40 ga bo‘ling.

$$Re(\frac{11}{10}+\frac{7}{10}i)$$

\frac{11}{10}+\frac{7}{10}i ning real qismi – \frac{11}{10}.

$$\frac{11}{10}$$