4-7i/3+5i eching

$$\frac { 4 - 7 i } { 3 + 5 i }$$

Baholash

$$-\frac{23}{34}-\frac{41}{34}i\approx -0,676470588-1,205882353i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 3-5i.

$$\frac{\left(4-7i\right)\left(3-5i\right)}{\left(3+5i\right)\left(3-5i\right)}$$

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

$$\frac{\left(4-7i\right)\left(3-5i\right)}{3^{2}-5^{2}i^{2}}$$

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

$$\frac{\left(4-7i\right)\left(3-5i\right)}{34}$$

Binomlarni ko‘paytirgandek 4-7i va 3-5i murakkab sonlarni ko‘paytiring.

$$\frac{4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)i^{2}}{34}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)\left(-1\right)}{34}$$

4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{12-20i-21i-35}{34}$$

12-20i-21i-35 ichida real va mavhum qismlarni birlashtiring.

$$\frac{12-35+\left(-20-21\right)i}{34}$$

12-35+\left(-20-21\right)i ichida qo‘shishlarni bajaring.

$$\frac{-23-41i}{34}$$

-\frac{23}{34}-\frac{41}{34}i ni olish uchun -23-41i ni 34 ga bo‘ling.

$$-\frac{23}{34}-\frac{41}{34}i$$

Ashyoviy qism

$$-\frac{23}{34} = -0,6764705882352942$$

Yechim qadamlari

\frac{4-7i}{3+5i}ning surat va maxrajini murakkab tutash maxraj 3-5i bilan ko‘paytiring.

$$Re(\frac{\left(4-7i\right)\left(3-5i\right)}{\left(3+5i\right)\left(3-5i\right)})$$

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

$$Re(\frac{\left(4-7i\right)\left(3-5i\right)}{3^{2}-5^{2}i^{2}})$$

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

$$Re(\frac{\left(4-7i\right)\left(3-5i\right)}{34})$$

Binomlarni ko‘paytirgandek 4-7i va 3-5i murakkab sonlarni ko‘paytiring.

$$Re(\frac{4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)i^{2}}{34})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)\left(-1\right)}{34})$$

4\times 3+4\times \left(-5i\right)-7i\times 3-7\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{12-20i-21i-35}{34})$$

12-20i-21i-35 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{12-35+\left(-20-21\right)i}{34})$$

12-35+\left(-20-21\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-23-41i}{34})$$

-\frac{23}{34}-\frac{41}{34}i ni olish uchun -23-41i ni 34 ga bo‘ling.

$$Re(-\frac{23}{34}-\frac{41}{34}i)$$

-\frac{23}{34}-\frac{41}{34}i ning real qismi – -\frac{23}{34}.

$$-\frac{23}{34}$$