15/3+4i eching

$$\frac { 15 } { 3 + 4 i }$$

Baholash

$$\frac{9}{5}-\frac{12}{5}i=1,8-2,4i$$

Yechim qadamlari

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

$$\frac{15\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}$$

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

$$\frac{15\left(3-4i\right)}{3^{2}-4^{2}i^{2}}$$

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

$$\frac{15\left(3-4i\right)}{25}$$

15 ni 3-4i marotabaga ko'paytirish.

$$\frac{15\times 3+15\times \left(-4i\right)}{25}$$

15\times 3+15\times \left(-4i\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{45-60i}{25}$$

\frac{9}{5}-\frac{12}{5}i ni olish uchun 45-60i ni 25 ga bo‘ling.

$$\frac{9}{5}-\frac{12}{5}i$$

Ashyoviy qism

$$\frac{9}{5} = 1\frac{4}{5} = 1,8$$

Yechim qadamlari

\frac{15}{3+4i}ning surat va maxrajini murakkab tutash maxraj 3-4i bilan ko‘paytiring.

$$Re(\frac{15\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)})$$

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

$$Re(\frac{15\left(3-4i\right)}{3^{2}-4^{2}i^{2}})$$

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

$$Re(\frac{15\left(3-4i\right)}{25})$$

15 ni 3-4i marotabaga ko'paytirish.

$$Re(\frac{15\times 3+15\times \left(-4i\right)}{25})$$

15\times 3+15\times \left(-4i\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{45-60i}{25})$$

\frac{9}{5}-\frac{12}{5}i ni olish uchun 45-60i ni 25 ga bo‘ling.

$$Re(\frac{9}{5}-\frac{12}{5}i)$$

\frac{9}{5}-\frac{12}{5}i ning real qismi – \frac{9}{5}.

$$\frac{9}{5}$$