4+2i/2-7i eching

$$\frac { 4 + 2 i } { 2 - 7 i }$$

Baholash

$$-\frac{6}{53}+\frac{32}{53}i\approx -0,113207547+0,603773585i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 2+7i.

$$\frac{\left(4+2i\right)\left(2+7i\right)}{\left(2-7i\right)\left(2+7i\right)}$$

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

$$\frac{\left(4+2i\right)\left(2+7i\right)}{2^{2}-7^{2}i^{2}}$$

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

$$\frac{\left(4+2i\right)\left(2+7i\right)}{53}$$

Binomlarni ko‘paytirgandek 4+2i va 2+7i murakkab sonlarni ko‘paytiring.

$$\frac{4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7i^{2}}{53}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7\left(-1\right)}{53}$$

4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{8+28i+4i-14}{53}$$

8+28i+4i-14 ichida real va mavhum qismlarni birlashtiring.

$$\frac{8-14+\left(28+4\right)i}{53}$$

8-14+\left(28+4\right)i ichida qo‘shishlarni bajaring.

$$\frac{-6+32i}{53}$$

-\frac{6}{53}+\frac{32}{53}i ni olish uchun -6+32i ni 53 ga bo‘ling.

$$-\frac{6}{53}+\frac{32}{53}i$$

Ashyoviy qism

$$-\frac{6}{53} = -0,11320754716981132$$

Yechim qadamlari

\frac{4+2i}{2-7i}ning surat va maxrajini murakkab tutash maxraj 2+7i bilan ko‘paytiring.

$$Re(\frac{\left(4+2i\right)\left(2+7i\right)}{\left(2-7i\right)\left(2+7i\right)})$$

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

$$Re(\frac{\left(4+2i\right)\left(2+7i\right)}{2^{2}-7^{2}i^{2}})$$

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

$$Re(\frac{\left(4+2i\right)\left(2+7i\right)}{53})$$

Binomlarni ko‘paytirgandek 4+2i va 2+7i murakkab sonlarni ko‘paytiring.

$$Re(\frac{4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7i^{2}}{53})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7\left(-1\right)}{53})$$

4\times 2+4\times \left(7i\right)+2i\times 2+2\times 7\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{8+28i+4i-14}{53})$$

8+28i+4i-14 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{8-14+\left(28+4\right)i}{53})$$

8-14+\left(28+4\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-6+32i}{53})$$

-\frac{6}{53}+\frac{32}{53}i ni olish uchun -6+32i ni 53 ga bo‘ling.

$$Re(-\frac{6}{53}+\frac{32}{53}i)$$

-\frac{6}{53}+\frac{32}{53}i ning real qismi – -\frac{6}{53}.

$$-\frac{6}{53}$$