2+3i/-1+i eching

$$\frac { 2 + 3 i } { - 1 + i }$$

Baholash

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

Yechim qadamlari

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

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{-2-2i-3i+3}{2}$$

-2-2i-3i+3 ichida real va mavhum qismlarni birlashtiring.

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

-2+3+\left(-2-3\right)i ichida qo‘shishlarni bajaring.

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

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

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

Ashyoviy qism

$$\frac{1}{2} = 0,5$$

Yechim qadamlari

\frac{2+3i}{-1+i}ning surat va maxrajini murakkab tutash maxraj -1-i bilan ko‘paytiring.

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

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

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

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

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

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

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

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{-2-2i-3i+3}{2})$$

-2-2i-3i+3 ichida real va mavhum qismlarni birlashtiring.

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

-2+3+\left(-2-3\right)i ichida qo‘shishlarni bajaring.

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

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

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

\frac{1}{2}-\frac{5}{2}i ning real qismi – \frac{1}{2}.

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