3-2i/4+5i eching

$$\frac { 3 - 2 i } { 4 + 5 i }$$

Baholash

$$\frac{2}{41}-\frac{23}{41}i\approx 0,048780488-0,56097561i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 4-5i.

$$\frac{\left(3-2i\right)\left(4-5i\right)}{\left(4+5i\right)\left(4-5i\right)}$$

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

$$\frac{\left(3-2i\right)\left(4-5i\right)}{4^{2}-5^{2}i^{2}}$$

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

$$\frac{\left(3-2i\right)\left(4-5i\right)}{41}$$

Binomlarni ko‘paytirgandek 3-2i va 4-5i murakkab sonlarni ko‘paytiring.

$$\frac{3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)i^{2}}{41}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)\left(-1\right)}{41}$$

3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{12-15i-8i-10}{41}$$

12-15i-8i-10 ichida real va mavhum qismlarni birlashtiring.

$$\frac{12-10+\left(-15-8\right)i}{41}$$

12-10+\left(-15-8\right)i ichida qo‘shishlarni bajaring.

$$\frac{2-23i}{41}$$

\frac{2}{41}-\frac{23}{41}i ni olish uchun 2-23i ni 41 ga bo‘ling.

$$\frac{2}{41}-\frac{23}{41}i$$

Ashyoviy qism

$$\frac{2}{41} = 0,04878048780487805$$

Yechim qadamlari

\frac{3-2i}{4+5i}ning surat va maxrajini murakkab tutash maxraj 4-5i bilan ko‘paytiring.

$$Re(\frac{\left(3-2i\right)\left(4-5i\right)}{\left(4+5i\right)\left(4-5i\right)})$$

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

$$Re(\frac{\left(3-2i\right)\left(4-5i\right)}{4^{2}-5^{2}i^{2}})$$

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

$$Re(\frac{\left(3-2i\right)\left(4-5i\right)}{41})$$

Binomlarni ko‘paytirgandek 3-2i va 4-5i murakkab sonlarni ko‘paytiring.

$$Re(\frac{3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)i^{2}}{41})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)\left(-1\right)}{41})$$

3\times 4+3\times \left(-5i\right)-2i\times 4-2\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{12-15i-8i-10}{41})$$

12-15i-8i-10 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{12-10+\left(-15-8\right)i}{41})$$

12-10+\left(-15-8\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{2-23i}{41})$$

\frac{2}{41}-\frac{23}{41}i ni olish uchun 2-23i ni 41 ga bo‘ling.

$$Re(\frac{2}{41}-\frac{23}{41}i)$$

\frac{2}{41}-\frac{23}{41}i ning real qismi – \frac{2}{41}.

$$\frac{2}{41}$$