4+3i/-1+5i eching

$$\frac { 4 + 3 i } { - 1 + 5 i }$$

Baholash

$$\frac{11}{26}-\frac{23}{26}i\approx 0,423076923-0,884615385i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, -1-5i.

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

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

$$\frac{\left(4+3i\right)\left(-1-5i\right)}{\left(-1\right)^{2}-5^{2}i^{2}}$$

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

$$\frac{\left(4+3i\right)\left(-1-5i\right)}{26}$$

Binomlarni ko‘paytirgandek 4+3i va -1-5i murakkab sonlarni ko‘paytiring.

$$\frac{4\left(-1\right)+4\times \left(-5i\right)+3i\left(-1\right)+3\left(-5\right)i^{2}}{26}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{4\left(-1\right)+4\times \left(-5i\right)+3i\left(-1\right)+3\left(-5\right)\left(-1\right)}{26}$$

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

$$\frac{-4-20i-3i+15}{26}$$

-4-20i-3i+15 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-4+15+\left(-20-3\right)i}{26}$$

-4+15+\left(-20-3\right)i ichida qo‘shishlarni bajaring.

$$\frac{11-23i}{26}$$

\frac{11}{26}-\frac{23}{26}i ni olish uchun 11-23i ni 26 ga bo‘ling.

$$\frac{11}{26}-\frac{23}{26}i$$

Ashyoviy qism

$$\frac{11}{26} = 0,4230769230769231$$

Yechim qadamlari

\frac{4+3i}{-1+5i}ning surat va maxrajini murakkab tutash maxraj -1-5i bilan ko‘paytiring.

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

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

$$Re(\frac{\left(4+3i\right)\left(-1-5i\right)}{\left(-1\right)^{2}-5^{2}i^{2}})$$

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

$$Re(\frac{\left(4+3i\right)\left(-1-5i\right)}{26})$$

Binomlarni ko‘paytirgandek 4+3i va -1-5i murakkab sonlarni ko‘paytiring.

$$Re(\frac{4\left(-1\right)+4\times \left(-5i\right)+3i\left(-1\right)+3\left(-5\right)i^{2}}{26})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{4\left(-1\right)+4\times \left(-5i\right)+3i\left(-1\right)+3\left(-5\right)\left(-1\right)}{26})$$

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

$$Re(\frac{-4-20i-3i+15}{26})$$

-4-20i-3i+15 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-4+15+\left(-20-3\right)i}{26})$$

-4+15+\left(-20-3\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{11-23i}{26})$$

\frac{11}{26}-\frac{23}{26}i ni olish uchun 11-23i ni 26 ga bo‘ling.

$$Re(\frac{11}{26}-\frac{23}{26}i)$$

\frac{11}{26}-\frac{23}{26}i ning real qismi – \frac{11}{26}.

$$\frac{11}{26}$$