3+5i/1-2i eching

$$\frac { 3 + 5 i } { 1 - 2 i }$$

Baholash

$$-\frac{7}{5}+\frac{11}{5}i=-1,4+2,2i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 1+2i.

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

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

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

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

$$\frac{\left(3+5i\right)\left(1+2i\right)}{5}$$

Binomlarni ko‘paytirgandek 3+5i va 1+2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{3+6i+5i-10}{5}$$

3+6i+5i-10 ichida real va mavhum qismlarni birlashtiring.

$$\frac{3-10+\left(6+5\right)i}{5}$$

3-10+\left(6+5\right)i ichida qo‘shishlarni bajaring.

$$\frac{-7+11i}{5}$$

-\frac{7}{5}+\frac{11}{5}i ni olish uchun -7+11i ni 5 ga bo‘ling.

$$-\frac{7}{5}+\frac{11}{5}i$$

Ashyoviy qism

$$-\frac{7}{5} = -1\frac{2}{5} = -1,4$$

Yechim qadamlari

\frac{3+5i}{1-2i}ning surat va maxrajini murakkab tutash maxraj 1+2i bilan ko‘paytiring.

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

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

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

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

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

Binomlarni ko‘paytirgandek 3+5i va 1+2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{3+6i+5i-10}{5})$$

3+6i+5i-10 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{3-10+\left(6+5\right)i}{5})$$

3-10+\left(6+5\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-7+11i}{5})$$

-\frac{7}{5}+\frac{11}{5}i ni olish uchun -7+11i ni 5 ga bo‘ling.

$$Re(-\frac{7}{5}+\frac{11}{5}i)$$

-\frac{7}{5}+\frac{11}{5}i ning real qismi – -\frac{7}{5}.

$$-\frac{7}{5}$$