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.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

1\times 1+1\times \left(2i\right)+2i\times 1+2\times 2\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.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

1\times 1+1\times \left(2i\right)+2i\times 1+2\times 2\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}.

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