1/2+3i eching

$$\frac { 1 } { 2 + 3 i }$$

Baholash

$$\frac{2}{13}-\frac{3}{13}i\approx 0,153846154-0,230769231i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 2-3i.

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

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

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

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

$$\frac{1\left(2-3i\right)}{13}$$

2-3i hosil qilish uchun 1 va 2-3i ni ko'paytirish.

$$\frac{2-3i}{13}$$

\frac{2}{13}-\frac{3}{13}i ni olish uchun 2-3i ni 13 ga bo‘ling.

$$\frac{2}{13}-\frac{3}{13}i$$

Ashyoviy qism

$$\frac{2}{13} = 0,15384615384615385$$

Yechim qadamlari

\frac{1}{2+3i}ning surat va maxrajini murakkab tutash maxraj 2-3i bilan ko‘paytiring.

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

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

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

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

$$Re(\frac{1\left(2-3i\right)}{13})$$

2-3i hosil qilish uchun 1 va 2-3i ni ko'paytirish.

$$Re(\frac{2-3i}{13})$$

\frac{2}{13}-\frac{3}{13}i ni olish uchun 2-3i ni 13 ga bo‘ling.

$$Re(\frac{2}{13}-\frac{3}{13}i)$$

\frac{2}{13}-\frac{3}{13}i ning real qismi – \frac{2}{13}.

$$\frac{2}{13}$$