1/4+3i eching

$$\frac { 1 } { 4 + 3 i }$$

Baholash

$$\frac{4}{25}-\frac{3}{25}i=0,16-0,12i$$

Yechim qadamlari

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

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

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

$$\frac{1\left(4-3i\right)}{4^{2}-3^{2}i^{2}}$$

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

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

4-3i hosil qilish uchun 1 va 4-3i ni ko'paytirish.

$$\frac{4-3i}{25}$$

\frac{4}{25}-\frac{3}{25}i ni olish uchun 4-3i ni 25 ga bo‘ling.

$$\frac{4}{25}-\frac{3}{25}i$$

Ashyoviy qism

$$\frac{4}{25} = 0,16$$

Yechim qadamlari

\frac{1}{4+3i}ning surat va maxrajini murakkab tutash maxraj 4-3i bilan ko‘paytiring.

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

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

$$Re(\frac{1\left(4-3i\right)}{4^{2}-3^{2}i^{2}})$$

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

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

4-3i hosil qilish uchun 1 va 4-3i ni ko'paytirish.

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

\frac{4}{25}-\frac{3}{25}i ni olish uchun 4-3i ni 25 ga bo‘ling.

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

\frac{4}{25}-\frac{3}{25}i ning real qismi – \frac{4}{25}.

$$\frac{4}{25}$$