-1-4i/-5-9i eching

$$\frac { - 1 - 4 i } { - 5 - 9 i }$$

Baholash

$$\frac{41}{106}+\frac{11}{106}i\approx 0,386792453+0,103773585i$$

Yechim qadamlari

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

$$\frac{\left(-1-4i\right)\left(-5+9i\right)}{\left(-5-9i\right)\left(-5+9i\right)}$$

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

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

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

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

Binomlarni ko‘paytirgandek -1-4i va -5+9i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{5-9i+20i+36}{106}$$

5-9i+20i+36 ichida real va mavhum qismlarni birlashtiring.

$$\frac{5+36+\left(-9+20\right)i}{106}$$

5+36+\left(-9+20\right)i ichida qo‘shishlarni bajaring.

$$\frac{41+11i}{106}$$

\frac{41}{106}+\frac{11}{106}i ni olish uchun 41+11i ni 106 ga bo‘ling.

$$\frac{41}{106}+\frac{11}{106}i$$

Ashyoviy qism

$$\frac{41}{106} = 0,3867924528301887$$

Yechim qadamlari

\frac{-1-4i}{-5-9i}ning surat va maxrajini murakkab tutash maxraj -5+9i bilan ko‘paytiring.

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

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

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

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

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

Binomlarni ko‘paytirgandek -1-4i va -5+9i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{5-9i+20i+36}{106})$$

5-9i+20i+36 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{5+36+\left(-9+20\right)i}{106})$$

5+36+\left(-9+20\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{41+11i}{106})$$

\frac{41}{106}+\frac{11}{106}i ni olish uchun 41+11i ni 106 ga bo‘ling.

$$Re(\frac{41}{106}+\frac{11}{106}i)$$

\frac{41}{106}+\frac{11}{106}i ning real qismi – \frac{41}{106}.

$$\frac{41}{106}$$