1/1+i+i eching

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

Baholash

$$\frac{1}{2}+\frac{1}{2}i=0,5+0,5i$$

Yechim qadamlari

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

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

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

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

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

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

1-i hosil qilish uchun 1 va 1-i ni ko'paytirish.

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

\frac{1}{2}-\frac{1}{2}i ni olish uchun 1-i ni 2 ga bo‘ling.

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

\frac{1}{2}-\frac{1}{2}i va i sonlari ichida real va mavhum qismlarni birlashtiring.

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

-\frac{1}{2} ni 1 ga qo'shish.

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

Ashyoviy qism

$$\frac{1}{2} = 0,5$$

Yechim qadamlari

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

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

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

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

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

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

1-i hosil qilish uchun 1 va 1-i ni ko'paytirish.

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

\frac{1}{2}-\frac{1}{2}i ni olish uchun 1-i ni 2 ga bo‘ling.

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

\frac{1}{2}-\frac{1}{2}i va i sonlari ichida real va mavhum qismlarni birlashtiring.

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

-\frac{1}{2} ni 1 ga qo'shish.

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

\frac{1}{2}+\frac{1}{2}i ning real qismi – \frac{1}{2}.

$$\frac{1}{2}$$