1/(3+2i) eching

$$1 / ( 3 + 2 i )$$

Baholash

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

Yechim qadamlari

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

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

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

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

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

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

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

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

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

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

Ashyoviy qism

$$\frac{3}{13} = 0,23076923076923078$$

Yechim qadamlari

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

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

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

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

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

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

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

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

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

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

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

$$\frac{3}{13}$$