1-2i/1+2i eching

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

Baholash

$$-\frac{3}{5}-\frac{4}{5}i=-0,6-0,8i$$

Yechim qadamlari

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

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

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

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

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

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

Binomlarni ko‘paytirgandek 1-2i va 1-2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{1-2i-2i-4}{5}$$

1-2i-2i-4 ichida real va mavhum qismlarni birlashtiring.

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

1-4+\left(-2-2\right)i ichida qo‘shishlarni bajaring.

$$\frac{-3-4i}{5}$$

-\frac{3}{5}-\frac{4}{5}i ni olish uchun -3-4i ni 5 ga bo‘ling.

$$-\frac{3}{5}-\frac{4}{5}i$$

Ashyoviy qism

$$-\frac{3}{5} = -0,6$$

Yechim qadamlari

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

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

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

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

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

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

Binomlarni ko‘paytirgandek 1-2i va 1-2i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{1-2i-2i-4}{5})$$

1-2i-2i-4 ichida real va mavhum qismlarni birlashtiring.

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

1-4+\left(-2-2\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-3-4i}{5})$$

-\frac{3}{5}-\frac{4}{5}i ni olish uchun -3-4i ni 5 ga bo‘ling.

$$Re(-\frac{3}{5}-\frac{4}{5}i)$$

-\frac{3}{5}-\frac{4}{5}i ning real qismi – -\frac{3}{5}.

$$-\frac{3}{5}$$