2/3+2i eching

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

Baholash

$$\frac{6}{13}-\frac{4}{13}i\approx 0,461538462-0,307692308i$$

Yechim qadamlari

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

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

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

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

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

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

2 ni 3-2i marotabaga ko'paytirish.

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

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

$$\frac{6-4i}{13}$$

\frac{6}{13}-\frac{4}{13}i ni olish uchun 6-4i ni 13 ga bo‘ling.

$$\frac{6}{13}-\frac{4}{13}i$$

Ashyoviy qism

$$\frac{6}{13} = 0,46153846153846156$$

Yechim qadamlari

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

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

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

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

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

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

2 ni 3-2i marotabaga ko'paytirish.

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

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

$$Re(\frac{6-4i}{13})$$

\frac{6}{13}-\frac{4}{13}i ni olish uchun 6-4i ni 13 ga bo‘ling.

$$Re(\frac{6}{13}-\frac{4}{13}i)$$

\frac{6}{13}-\frac{4}{13}i ning real qismi – \frac{6}{13}.

$$\frac{6}{13}$$