-2-4i/5+9i eching

$$\frac { - 2 - 4 i } { 5 + 9 i }$$

Baholash

$$-\frac{23}{53}-\frac{1}{53}i\approx -0,433962264-0,018867925i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 5-9i.

$$\frac{\left(-2-4i\right)\left(5-9i\right)}{\left(5+9i\right)\left(5-9i\right)}$$

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

$$\frac{\left(-2-4i\right)\left(5-9i\right)}{5^{2}-9^{2}i^{2}}$$

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

$$\frac{\left(-2-4i\right)\left(5-9i\right)}{106}$$

Binomlarni ko‘paytirgandek -2-4i va 5-9i murakkab sonlarni ko‘paytiring.

$$\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)i^{2}}{106}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right)}{106}$$

-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-10+18i-20i-36}{106}$$

-10+18i-20i-36 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-10-36+\left(18-20\right)i}{106}$$

-10-36+\left(18-20\right)i ichida qo‘shishlarni bajaring.

$$\frac{-46-2i}{106}$$

-\frac{23}{53}-\frac{1}{53}i ni olish uchun -46-2i ni 106 ga bo‘ling.

$$-\frac{23}{53}-\frac{1}{53}i$$

Ashyoviy qism

$$-\frac{23}{53} = -0,4339622641509434$$

Yechim qadamlari

\frac{-2-4i}{5+9i}ning surat va maxrajini murakkab tutash maxraj 5-9i bilan ko‘paytiring.

$$Re(\frac{\left(-2-4i\right)\left(5-9i\right)}{\left(5+9i\right)\left(5-9i\right)})$$

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

$$Re(\frac{\left(-2-4i\right)\left(5-9i\right)}{5^{2}-9^{2}i^{2}})$$

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

$$Re(\frac{\left(-2-4i\right)\left(5-9i\right)}{106})$$

Binomlarni ko‘paytirgandek -2-4i va 5-9i murakkab sonlarni ko‘paytiring.

$$Re(\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)i^{2}}{106})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right)}{106})$$

-2\times 5-2\times \left(-9i\right)-4i\times 5-4\left(-9\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-10+18i-20i-36}{106})$$

-10+18i-20i-36 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-10-36+\left(18-20\right)i}{106})$$

-10-36+\left(18-20\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-46-2i}{106})$$

-\frac{23}{53}-\frac{1}{53}i ni olish uchun -46-2i ni 106 ga bo‘ling.

$$Re(-\frac{23}{53}-\frac{1}{53}i)$$

-\frac{23}{53}-\frac{1}{53}i ning real qismi – -\frac{23}{53}.

$$-\frac{23}{53}$$