5+i/1-i eching

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

Baholash

$$2+3i$$

Yechim qadamlari

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

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

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

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

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

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

Binomlarni ko‘paytirgandek 5+i va 1+i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

5\times 1+5i+i-1 ichidagi ko‘paytirishlarni bajaring.

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

5+5i+i-1 ichida real va mavhum qismlarni birlashtiring.

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

5-1+\left(5+1\right)i ichida qo‘shishlarni bajaring.

$$\frac{4+6i}{2}$$

2+3i ni olish uchun 4+6i ni 2 ga bo‘ling.

$$2+3i$$

Ashyoviy qism

$$2$$

Yechim qadamlari

\frac{5+i}{1-i}ning surat va maxrajini murakkab tutash maxraj 1+i bilan ko‘paytiring.

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

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

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

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

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

Binomlarni ko‘paytirgandek 5+i va 1+i murakkab sonlarni ko‘paytiring.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

5\times 1+5i+i-1 ichidagi ko‘paytirishlarni bajaring.

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

5+5i+i-1 ichida real va mavhum qismlarni birlashtiring.

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

5-1+\left(5+1\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{4+6i}{2})$$

2+3i ni olish uchun 4+6i ni 2 ga bo‘ling.

$$Re(2+3i)$$

2+3i ning real qismi – 2.

$$2$$