3+i/-1+4i eching

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

Baholash

$$\frac{1}{17}-\frac{13}{17}i\approx 0,058823529-0,764705882i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, -1-4i.

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

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

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

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

$$\frac{\left(3+i\right)\left(-1-4i\right)}{17}$$

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

$$\frac{3\left(-1\right)+3\times \left(-4i\right)-i-4i^{2}}{17}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{3\left(-1\right)+3\times \left(-4i\right)-i-4\left(-1\right)}{17}$$

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

$$\frac{-3-12i-i+4}{17}$$

-3-12i-i+4 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-3+4+\left(-12-1\right)i}{17}$$

-3+4+\left(-12-1\right)i ichida qo‘shishlarni bajaring.

$$\frac{1-13i}{17}$$

\frac{1}{17}-\frac{13}{17}i ni olish uchun 1-13i ni 17 ga bo‘ling.

$$\frac{1}{17}-\frac{13}{17}i$$

Ashyoviy qism

$$\frac{1}{17} = 0,058823529411764705$$

Yechim qadamlari

\frac{3+i}{-1+4i}ning surat va maxrajini murakkab tutash maxraj -1-4i bilan ko‘paytiring.

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

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

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

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

$$Re(\frac{\left(3+i\right)\left(-1-4i\right)}{17})$$

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

$$Re(\frac{3\left(-1\right)+3\times \left(-4i\right)-i-4i^{2}}{17})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{3\left(-1\right)+3\times \left(-4i\right)-i-4\left(-1\right)}{17})$$

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

$$Re(\frac{-3-12i-i+4}{17})$$

-3-12i-i+4 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-3+4+\left(-12-1\right)i}{17})$$

-3+4+\left(-12-1\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{1-13i}{17})$$

\frac{1}{17}-\frac{13}{17}i ni olish uchun 1-13i ni 17 ga bo‘ling.

$$Re(\frac{1}{17}-\frac{13}{17}i)$$

\frac{1}{17}-\frac{13}{17}i ning real qismi – \frac{1}{17}.

$$\frac{1}{17}$$