1*1/1+i eching

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

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.

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

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

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

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

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

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

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

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

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

\frac{1}{2}-\frac{1}{2}i hosil qilish uchun 1 va \frac{1}{2}-\frac{1}{2}i ni ko'paytirish.

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

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.

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

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

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

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

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

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

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

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

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

\frac{1}{2}-\frac{1}{2}i hosil qilish uchun 1 va \frac{1}{2}-\frac{1}{2}i ni ko'paytirish.

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

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

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