(3+4i)(1+2i)/1+i= eching

$$\frac { ( 3 + 4 i ) ( 1 + 2 i ) } { 1 + i } =$$

Baholash

$$\frac{5}{2}+\frac{15}{2}i=2,5+7,5i$$

Yechim qadamlari

Binomlarni ko‘paytirgandek 3+4i va 1+2i murakkab sonlarni ko‘paytiring.

$$\frac{3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2i^{2}}{1+i}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2\left(-1\right)}{1+i}$$

3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3+6i+4i-8}{1+i}$$

3+6i+4i-8 ichida real va mavhum qismlarni birlashtiring.

$$\frac{3-8+\left(6+4\right)i}{1+i}$$

3-8+\left(6+4\right)i ichida qo‘shishlarni bajaring.

$$\frac{-5+10i}{1+i}$$

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

$$\frac{\left(-5+10i\right)\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}$$

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

$$\frac{\left(-5+10i\right)\left(1-i\right)}{1^{2}-i^{2}}$$

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

$$\frac{\left(-5+10i\right)\left(1-i\right)}{2}$$

Binomlarni ko‘paytirgandek -5+10i va 1-i murakkab sonlarni ko‘paytiring.

$$\frac{-5-5\left(-i\right)+10i\times 1+10\left(-1\right)i^{2}}{2}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{-5-5\left(-i\right)+10i\times 1+10\left(-1\right)\left(-1\right)}{2}$$

-5-5\left(-i\right)+10i\times 1+10\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-5+5i+10i+10}{2}$$

-5+5i+10i+10 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-5+10+\left(5+10\right)i}{2}$$

-5+10+\left(5+10\right)i ichida qo‘shishlarni bajaring.

$$\frac{5+15i}{2}$$

\frac{5}{2}+\frac{15}{2}i ni olish uchun 5+15i ni 2 ga bo‘ling.

$$\frac{5}{2}+\frac{15}{2}i$$

Ashyoviy qism

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

Yechim qadamlari

Binomlarni ko‘paytirgandek 3+4i va 1+2i murakkab sonlarni ko‘paytiring.

$$Re(\frac{3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2i^{2}}{1+i})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2\left(-1\right)}{1+i})$$

3\times 1+3\times \left(2i\right)+4i\times 1+4\times 2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{3+6i+4i-8}{1+i})$$

3+6i+4i-8 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{3-8+\left(6+4\right)i}{1+i})$$

3-8+\left(6+4\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-5+10i}{1+i})$$

\frac{-5+10i}{1+i}ning surat va maxrajini murakkab tutash maxraj 1-i bilan ko‘paytiring.

$$Re(\frac{\left(-5+10i\right)\left(1-i\right)}{\left(1+i\right)\left(1-i\right)})$$

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

$$Re(\frac{\left(-5+10i\right)\left(1-i\right)}{1^{2}-i^{2}})$$

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

$$Re(\frac{\left(-5+10i\right)\left(1-i\right)}{2})$$

Binomlarni ko‘paytirgandek -5+10i va 1-i murakkab sonlarni ko‘paytiring.

$$Re(\frac{-5-5\left(-i\right)+10i\times 1+10\left(-1\right)i^{2}}{2})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{-5-5\left(-i\right)+10i\times 1+10\left(-1\right)\left(-1\right)}{2})$$

-5-5\left(-i\right)+10i\times 1+10\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-5+5i+10i+10}{2})$$

-5+5i+10i+10 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-5+10+\left(5+10\right)i}{2})$$

-5+10+\left(5+10\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{5+15i}{2})$$

\frac{5}{2}+\frac{15}{2}i ni olish uchun 5+15i ni 2 ga bo‘ling.

$$Re(\frac{5}{2}+\frac{15}{2}i)$$

\frac{5}{2}+\frac{15}{2}i ning real qismi – \frac{5}{2}.

$$\frac{5}{2}$$