=1+i/1-i eching

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

Baholash

$$i$$

Yechim qadamlari

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

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

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

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

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

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

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

$$\frac{1\times 1+i+i+i^{2}}{2}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

1\times 1+i+i-1 ichidagi ko‘paytirishlarni bajaring.

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

1+i+i-1 ichida real va mavhum qismlarni birlashtiring.

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

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

$$\frac{2i}{2}$$

i ni olish uchun 2i ni 2 ga bo‘ling.

$$i$$

Ashyoviy qism

$$0$$

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

1\times 1+i+i-1 ichidagi ko‘paytirishlarni bajaring.

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

1+i+i-1 ichida real va mavhum qismlarni birlashtiring.

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

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

$$Re(\frac{2i}{2})$$

i ni olish uchun 2i ni 2 ga bo‘ling.

$$Re(i)$$

i ning real qismi – 0.

$$0$$