1/2-i+1-i/i(1+i) eching

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

Baholash

$$-\frac{3}{5}+\frac{1}{5}i=-0,6+0,2i$$

Yechim qadamlari

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

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

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

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

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

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

2+i hosil qilish uchun 1 va 2+i ni ko'paytirish.

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

\frac{2}{5}+\frac{1}{5}i ni olish uchun 2+i ni 5 ga bo‘ling.

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

i ni 1+i marotabaga ko'paytirish.

$$\frac{2}{5}+\frac{1}{5}i+\frac{1-i}{i+i^{2}}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

Shartlarni qayta saralash.

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

-1 ni olish uchun 1-i ni -1+i ga bo‘ling.

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

1 ni \frac{2}{5}+\frac{1}{5}i dan mos real va mavhum qismlarni ayirish orqali ayiring.

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

-\frac{3}{5} olish uchun \frac{2}{5} dan 1 ni ayirish.

$$-\frac{3}{5}+\frac{1}{5}i$$

Ashyoviy qism

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

Yechim qadamlari

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

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

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

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

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

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

2+i hosil qilish uchun 1 va 2+i ni ko'paytirish.

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

\frac{2}{5}+\frac{1}{5}i ni olish uchun 2+i ni 5 ga bo‘ling.

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

i ni 1+i marotabaga ko'paytirish.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

Shartlarni qayta saralash.

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

-1 ni olish uchun 1-i ni -1+i ga bo‘ling.

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

1 ni \frac{2}{5}+\frac{1}{5}i dan mos real va mavhum qismlarni ayirish orqali ayiring.

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

-\frac{3}{5} olish uchun \frac{2}{5} dan 1 ni ayirish.

$$Re(-\frac{3}{5}+\frac{1}{5}i)$$

-\frac{3}{5}+\frac{1}{5}i ning real qismi – -\frac{3}{5}.

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