3-4i/3+4i eching

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

Baholash

$$-\frac{7}{25}-\frac{24}{25}i=-0,28-0,96i$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{9-12i-12i-16}{25}$$

9-12i-12i-16 ichida real va mavhum qismlarni birlashtiring.

$$\frac{9-16+\left(-12-12\right)i}{25}$$

9-16+\left(-12-12\right)i ichida qo‘shishlarni bajaring.

$$\frac{-7-24i}{25}$$

-\frac{7}{25}-\frac{24}{25}i ni olish uchun -7-24i ni 25 ga bo‘ling.

$$-\frac{7}{25}-\frac{24}{25}i$$

Ashyoviy qism

$$-\frac{7}{25} = -0,28$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{9-12i-12i-16}{25})$$

9-12i-12i-16 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{9-16+\left(-12-12\right)i}{25})$$

9-16+\left(-12-12\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-7-24i}{25})$$

-\frac{7}{25}-\frac{24}{25}i ni olish uchun -7-24i ni 25 ga bo‘ling.

$$Re(-\frac{7}{25}-\frac{24}{25}i)$$

-\frac{7}{25}-\frac{24}{25}i ning real qismi – -\frac{7}{25}.

$$-\frac{7}{25}$$