7-3i/4-3i eching

$$\frac { 7 - 3 i } { 4 - 3 i }$$

Baholash

$$\frac{37}{25}+\frac{9}{25}i=1,48+0,36i$$

Yechim qadamlari

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

$$\frac{\left(7-3i\right)\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)}$$

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

$$\frac{\left(7-3i\right)\left(4+3i\right)}{4^{2}-3^{2}i^{2}}$$

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

$$\frac{\left(7-3i\right)\left(4+3i\right)}{25}$$

Binomlarni ko‘paytirgandek 7-3i va 4+3i murakkab sonlarni ko‘paytiring.

$$\frac{7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3i^{2}}{25}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3\left(-1\right)}{25}$$

7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{28+21i-12i+9}{25}$$

28+21i-12i+9 ichida real va mavhum qismlarni birlashtiring.

$$\frac{28+9+\left(21-12\right)i}{25}$$

28+9+\left(21-12\right)i ichida qo‘shishlarni bajaring.

$$\frac{37+9i}{25}$$

\frac{37}{25}+\frac{9}{25}i ni olish uchun 37+9i ni 25 ga bo‘ling.

$$\frac{37}{25}+\frac{9}{25}i$$

Ashyoviy qism

$$\frac{37}{25} = 1\frac{12}{25} = 1,48$$

Yechim qadamlari

\frac{7-3i}{4-3i}ning surat va maxrajini murakkab tutash maxraj 4+3i bilan ko‘paytiring.

$$Re(\frac{\left(7-3i\right)\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)})$$

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

$$Re(\frac{\left(7-3i\right)\left(4+3i\right)}{4^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{\left(7-3i\right)\left(4+3i\right)}{25})$$

Binomlarni ko‘paytirgandek 7-3i va 4+3i murakkab sonlarni ko‘paytiring.

$$Re(\frac{7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3i^{2}}{25})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3\left(-1\right)}{25})$$

7\times 4+7\times \left(3i\right)-3i\times 4-3\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{28+21i-12i+9}{25})$$

28+21i-12i+9 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{28+9+\left(21-12\right)i}{25})$$

28+9+\left(21-12\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{37+9i}{25})$$

\frac{37}{25}+\frac{9}{25}i ni olish uchun 37+9i ni 25 ga bo‘ling.

$$Re(\frac{37}{25}+\frac{9}{25}i)$$

\frac{37}{25}+\frac{9}{25}i ning real qismi – \frac{37}{25}.

$$\frac{37}{25}$$