5+i/4+i eching

$$\frac { 5 + i } { 4 + i }$$

Baholash

$$\frac{21}{17}-\frac{1}{17}i\approx 1,235294118-0,058823529i$$

Yechim qadamlari

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

$$\frac{\left(5+i\right)\left(4-i\right)}{\left(4+i\right)\left(4-i\right)}$$

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

$$\frac{\left(5+i\right)\left(4-i\right)}{4^{2}-i^{2}}$$

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

$$\frac{\left(5+i\right)\left(4-i\right)}{17}$$

Binomlarni ko‘paytirgandek 5+i va 4-i murakkab sonlarni ko‘paytiring.

$$\frac{5\times 4+5\left(-i\right)+4i-i^{2}}{17}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{5\times 4+5\left(-i\right)+4i-\left(-1\right)}{17}$$

5\times 4+5\left(-i\right)+4i-\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{20-5i+4i+1}{17}$$

20-5i+4i+1 ichida real va mavhum qismlarni birlashtiring.

$$\frac{20+1+\left(-5+4\right)i}{17}$$

20+1+\left(-5+4\right)i ichida qo‘shishlarni bajaring.

$$\frac{21-i}{17}$$

\frac{21}{17}-\frac{1}{17}i ni olish uchun 21-i ni 17 ga bo‘ling.

$$\frac{21}{17}-\frac{1}{17}i$$

Ashyoviy qism

$$\frac{21}{17} = 1\frac{4}{17} = 1,2352941176470589$$

Yechim qadamlari

\frac{5+i}{4+i}ning surat va maxrajini murakkab tutash maxraj 4-i bilan ko‘paytiring.

$$Re(\frac{\left(5+i\right)\left(4-i\right)}{\left(4+i\right)\left(4-i\right)})$$

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

$$Re(\frac{\left(5+i\right)\left(4-i\right)}{4^{2}-i^{2}})$$

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

$$Re(\frac{\left(5+i\right)\left(4-i\right)}{17})$$

Binomlarni ko‘paytirgandek 5+i va 4-i murakkab sonlarni ko‘paytiring.

$$Re(\frac{5\times 4+5\left(-i\right)+4i-i^{2}}{17})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{5\times 4+5\left(-i\right)+4i-\left(-1\right)}{17})$$

5\times 4+5\left(-i\right)+4i-\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{20-5i+4i+1}{17})$$

20-5i+4i+1 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{20+1+\left(-5+4\right)i}{17})$$

20+1+\left(-5+4\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{21-i}{17})$$

\frac{21}{17}-\frac{1}{17}i ni olish uchun 21-i ni 17 ga bo‘ling.

$$Re(\frac{21}{17}-\frac{1}{17}i)$$

\frac{21}{17}-\frac{1}{17}i ning real qismi – \frac{21}{17}.

$$\frac{21}{17}$$