104i/5+i eching

$$\frac { 104 i } { 5 + i }$$

Baholash

$$4+20i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 5-i.

$$\frac{104i\left(5-i\right)}{\left(5+i\right)\left(5-i\right)}$$

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

$$\frac{104i\left(5-i\right)}{5^{2}-i^{2}}$$

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

$$\frac{104i\left(5-i\right)}{26}$$

104i ni 5-i marotabaga ko'paytirish.

$$\frac{104i\times 5+104\left(-1\right)i^{2}}{26}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{104i\times 5+104\left(-1\right)\left(-1\right)}{26}$$

104i\times 5+104\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

$$\frac{104+520i}{26}$$

4+20i ni olish uchun 104+520i ni 26 ga bo‘ling.

$$4+20i$$

Ashyoviy qism

$$4$$

Yechim qadamlari

\frac{104i}{5+i}ning surat va maxrajini murakkab tutash maxraj 5-i bilan ko‘paytiring.

$$Re(\frac{104i\left(5-i\right)}{\left(5+i\right)\left(5-i\right)})$$

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

$$Re(\frac{104i\left(5-i\right)}{5^{2}-i^{2}})$$

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

$$Re(\frac{104i\left(5-i\right)}{26})$$

104i ni 5-i marotabaga ko'paytirish.

$$Re(\frac{104i\times 5+104\left(-1\right)i^{2}}{26})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{104i\times 5+104\left(-1\right)\left(-1\right)}{26})$$

104i\times 5+104\left(-1\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

$$Re(\frac{104+520i}{26})$$

4+20i ni olish uchun 104+520i ni 26 ga bo‘ling.

$$Re(4+20i)$$

4+20i ning real qismi – 4.

$$4$$