(8-5i)div(3+4i) eching

$$( 8 - 5 i ) \div ( 3 + 4 i )$$

Baholash

$$\frac{4}{25}-\frac{47}{25}i=0,16-1,88i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 3-4i.

$$\frac{\left(8-5i\right)\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}$$

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

$$\frac{\left(8-5i\right)\left(3-4i\right)}{3^{2}-4^{2}i^{2}}$$

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

$$\frac{\left(8-5i\right)\left(3-4i\right)}{25}$$

Binomlarni ko‘paytirgandek 8-5i va 3-4i murakkab sonlarni ko‘paytiring.

$$\frac{8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)i^{2}}{25}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)\left(-1\right)}{25}$$

8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{24-32i-15i-20}{25}$$

24-32i-15i-20 ichida real va mavhum qismlarni birlashtiring.

$$\frac{24-20+\left(-32-15\right)i}{25}$$

24-20+\left(-32-15\right)i ichida qo‘shishlarni bajaring.

$$\frac{4-47i}{25}$$

\frac{4}{25}-\frac{47}{25}i ni olish uchun 4-47i ni 25 ga bo‘ling.

$$\frac{4}{25}-\frac{47}{25}i$$

Ashyoviy qism

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

Yechim qadamlari

\frac{8-5i}{3+4i}ning surat va maxrajini murakkab tutash maxraj 3-4i bilan ko‘paytiring.

$$Re(\frac{\left(8-5i\right)\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)})$$

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

$$Re(\frac{\left(8-5i\right)\left(3-4i\right)}{3^{2}-4^{2}i^{2}})$$

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

$$Re(\frac{\left(8-5i\right)\left(3-4i\right)}{25})$$

Binomlarni ko‘paytirgandek 8-5i va 3-4i murakkab sonlarni ko‘paytiring.

$$Re(\frac{8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)i^{2}}{25})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)\left(-1\right)}{25})$$

8\times 3+8\times \left(-4i\right)-5i\times 3-5\left(-4\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{24-32i-15i-20}{25})$$

24-32i-15i-20 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{24-20+\left(-32-15\right)i}{25})$$

24-20+\left(-32-15\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{4-47i}{25})$$

\frac{4}{25}-\frac{47}{25}i ni olish uchun 4-47i ni 25 ga bo‘ling.

$$Re(\frac{4}{25}-\frac{47}{25}i)$$

\frac{4}{25}-\frac{47}{25}i ning real qismi – \frac{4}{25}.

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