5+5i/-6-3i eching

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

Baholash

$$-1-\frac{1}{3}i\approx -1-0,333333333i$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{-30+15i-30i-15}{45}$$

-30+15i-30i-15 ichida real va mavhum qismlarni birlashtiring.

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

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

$$\frac{-45-15i}{45}$$

-1-\frac{1}{3}i ni olish uchun -45-15i ni 45 ga bo‘ling.

$$-1-\frac{1}{3}i$$

Ashyoviy qism

$$-1$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

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

-30+15i-30i-15 ichida real va mavhum qismlarni birlashtiring.

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

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

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

-1-\frac{1}{3}i ni olish uchun -45-15i ni 45 ga bo‘ling.

$$Re(-1-\frac{1}{3}i)$$

-1-\frac{1}{3}i ning real qismi – -1.

$$-1$$