i/2+3i eching

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

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, 2-3i.

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

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

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

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

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

i ni 2-3i marotabaga ko'paytirish.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

2i-3\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

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

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

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

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

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

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

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

i ni 2-3i marotabaga ko'paytirish.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

2i-3\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

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

\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}.

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