-1+19/2i/8-3i eching

$$\frac{ -1+ \frac{ 19 }{ 2 } i }{ 8-3i }$$

Baholash

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

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 8+3i.

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{\left(8-3i\right)\left(8+3i\right)}$$

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

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{8^{2}-3^{2}i^{2}}$$

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

$$\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{73}$$

Binomlarni ko‘paytirgandek -1+\frac{19}{2}i va 8+3i murakkab sonlarni ko‘paytiring.

$$\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3i^{2}}{73}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right)}{73}$$

-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-8-3i+76i-\frac{57}{2}}{73}$$

-8-3i+76i-\frac{57}{2} ichida real va mavhum qismlarni birlashtiring.

$$\frac{-8-\frac{57}{2}+\left(-3+76\right)i}{73}$$

-8-\frac{57}{2}+\left(-3+76\right)i ichida qo‘shishlarni bajaring.

$$\frac{-\frac{73}{2}+73i}{73}$$

-\frac{1}{2}+i ni olish uchun -\frac{73}{2}+73i ni 73 ga bo‘ling.

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

Ashyoviy qism

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

Yechim qadamlari

\frac{-1+\frac{19}{2}i}{8-3i}ning surat va maxrajini murakkab tutash maxraj 8+3i bilan ko‘paytiring.

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{\left(8-3i\right)\left(8+3i\right)})$$

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

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{8^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{\left(-1+\frac{19}{2}i\right)\left(8+3i\right)}{73})$$

Binomlarni ko‘paytirgandek -1+\frac{19}{2}i va 8+3i murakkab sonlarni ko‘paytiring.

$$Re(\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3i^{2}}{73})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right)}{73})$$

-8-3i+\frac{19}{2}i\times 8+\frac{19}{2}\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-8-3i+76i-\frac{57}{2}}{73})$$

-8-3i+76i-\frac{57}{2} ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-8-\frac{57}{2}+\left(-3+76\right)i}{73})$$

-8-\frac{57}{2}+\left(-3+76\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-\frac{73}{2}+73i}{73})$$

-\frac{1}{2}+i ni olish uchun -\frac{73}{2}+73i ni 73 ga bo‘ling.

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

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

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