5-8i/3+6i eching

$$\frac { 5 - 8 i } { 3 + 6 i }$$

Baholash

$$-\frac{11}{15}-\frac{6}{5}i\approx -0,733333333-1,2i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 3-6i.

$$\frac{\left(5-8i\right)\left(3-6i\right)}{\left(3+6i\right)\left(3-6i\right)}$$

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

$$\frac{\left(5-8i\right)\left(3-6i\right)}{3^{2}-6^{2}i^{2}}$$

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

$$\frac{\left(5-8i\right)\left(3-6i\right)}{45}$$

Binomlarni ko‘paytirgandek 5-8i va 3-6i murakkab sonlarni ko‘paytiring.

$$\frac{5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)i^{2}}{45}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)\left(-1\right)}{45}$$

5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{15-30i-24i-48}{45}$$

15-30i-24i-48 ichida real va mavhum qismlarni birlashtiring.

$$\frac{15-48+\left(-30-24\right)i}{45}$$

15-48+\left(-30-24\right)i ichida qo‘shishlarni bajaring.

$$\frac{-33-54i}{45}$$

-\frac{11}{15}-\frac{6}{5}i ni olish uchun -33-54i ni 45 ga bo‘ling.

$$-\frac{11}{15}-\frac{6}{5}i$$

Ashyoviy qism

$$-\frac{11}{15} = -0,7333333333333333$$

Yechim qadamlari

\frac{5-8i}{3+6i}ning surat va maxrajini murakkab tutash maxraj 3-6i bilan ko‘paytiring.

$$Re(\frac{\left(5-8i\right)\left(3-6i\right)}{\left(3+6i\right)\left(3-6i\right)})$$

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

$$Re(\frac{\left(5-8i\right)\left(3-6i\right)}{3^{2}-6^{2}i^{2}})$$

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

$$Re(\frac{\left(5-8i\right)\left(3-6i\right)}{45})$$

Binomlarni ko‘paytirgandek 5-8i va 3-6i murakkab sonlarni ko‘paytiring.

$$Re(\frac{5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)i^{2}}{45})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)\left(-1\right)}{45})$$

5\times 3+5\times \left(-6i\right)-8i\times 3-8\left(-6\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{15-30i-24i-48}{45})$$

15-30i-24i-48 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{15-48+\left(-30-24\right)i}{45})$$

15-48+\left(-30-24\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-33-54i}{45})$$

-\frac{11}{15}-\frac{6}{5}i ni olish uchun -33-54i ni 45 ga bo‘ling.

$$Re(-\frac{11}{15}-\frac{6}{5}i)$$

-\frac{11}{15}-\frac{6}{5}i ning real qismi – -\frac{11}{15}.

$$-\frac{11}{15}$$