7+4i/5+3i eching

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

Baholash

$$\frac{47}{34}-\frac{1}{34}i\approx 1,382352941-0,029411765i$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

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

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

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

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

$$\frac{47-i}{34}$$

\frac{47}{34}-\frac{1}{34}i ni olish uchun 47-i ni 34 ga bo‘ling.

$$\frac{47}{34}-\frac{1}{34}i$$

Ashyoviy qism

$$\frac{47}{34} = 1\frac{13}{34} = 1,3823529411764706$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

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

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

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

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

$$Re(\frac{47-i}{34})$$

\frac{47}{34}-\frac{1}{34}i ni olish uchun 47-i ni 34 ga bo‘ling.

$$Re(\frac{47}{34}-\frac{1}{34}i)$$

\frac{47}{34}-\frac{1}{34}i ning real qismi – \frac{47}{34}.

$$\frac{47}{34}$$