2+3i/5-4i eching

$$\frac{ 2+3i }{ 5-4i }$$

Baholash

$$-\frac{2}{41}+\frac{23}{41}i\approx -0,048780488+0,56097561i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 5+4i.

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

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

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

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

$$\frac{\left(2+3i\right)\left(5+4i\right)}{41}$$

Binomlarni ko‘paytirgandek 2+3i va 5+4i murakkab sonlarni ko‘paytiring.

$$\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4i^{2}}{41}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right)}{41}$$

2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{10+8i+15i-12}{41}$$

10+8i+15i-12 ichida real va mavhum qismlarni birlashtiring.

$$\frac{10-12+\left(8+15\right)i}{41}$$

10-12+\left(8+15\right)i ichida qo‘shishlarni bajaring.

$$\frac{-2+23i}{41}$$

-\frac{2}{41}+\frac{23}{41}i ni olish uchun -2+23i ni 41 ga bo‘ling.

$$-\frac{2}{41}+\frac{23}{41}i$$

Ashyoviy qism

$$-\frac{2}{41} = -0,04878048780487805$$

Yechim qadamlari

\frac{2+3i}{5-4i}ning surat va maxrajini murakkab tutash maxraj 5+4i bilan ko‘paytiring.

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

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

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

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

$$Re(\frac{\left(2+3i\right)\left(5+4i\right)}{41})$$

Binomlarni ko‘paytirgandek 2+3i va 5+4i murakkab sonlarni ko‘paytiring.

$$Re(\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4i^{2}}{41})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right)}{41})$$

2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{10+8i+15i-12}{41})$$

10+8i+15i-12 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{10-12+\left(8+15\right)i}{41})$$

10-12+\left(8+15\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-2+23i}{41})$$

-\frac{2}{41}+\frac{23}{41}i ni olish uchun -2+23i ni 41 ga bo‘ling.

$$Re(-\frac{2}{41}+\frac{23}{41}i)$$

-\frac{2}{41}+\frac{23}{41}i ning real qismi – -\frac{2}{41}.

$$-\frac{2}{41}$$