2i/1+i eching

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

Baholash

$$1+i$$

Yechim qadamlari

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

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

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

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

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

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

2i ni 1-i marotabaga ko'paytirish.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

2i\times 1+2\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

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

1+i ni olish uchun 2+2i ni 2 ga bo‘ling.

$$1+i$$

Ashyoviy qism

$$1$$

Yechim qadamlari

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

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

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

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

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

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

2i ni 1-i marotabaga ko'paytirish.

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

2i\times 1+2\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

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

1+i ni olish uchun 2+2i ni 2 ga bo‘ling.

$$Re(1+i)$$

1+i ning real qismi – 1.

$$1$$