7+i/-7+6i= eching

$$\frac { 7 + i } { - 7 + 6 i } =$$

Baholash

$$-\frac{43}{85}-\frac{49}{85}i\approx -0,505882353-0,576470588i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, -7-6i.

$$\frac{\left(7+i\right)\left(-7-6i\right)}{\left(-7+6i\right)\left(-7-6i\right)}$$

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

$$\frac{\left(7+i\right)\left(-7-6i\right)}{\left(-7\right)^{2}-6^{2}i^{2}}$$

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

$$\frac{\left(7+i\right)\left(-7-6i\right)}{85}$$

Binomlarni ko‘paytirgandek 7+i va -7-6i murakkab sonlarni ko‘paytiring.

$$\frac{7\left(-7\right)+7\times \left(-6i\right)-7i-6i^{2}}{85}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{7\left(-7\right)+7\times \left(-6i\right)-7i-6\left(-1\right)}{85}$$

7\left(-7\right)+7\times \left(-6i\right)-7i-6\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-49-42i-7i+6}{85}$$

-49-42i-7i+6 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-49+6+\left(-42-7\right)i}{85}$$

-49+6+\left(-42-7\right)i ichida qo‘shishlarni bajaring.

$$\frac{-43-49i}{85}$$

-\frac{43}{85}-\frac{49}{85}i ni olish uchun -43-49i ni 85 ga bo‘ling.

$$-\frac{43}{85}-\frac{49}{85}i$$

Ashyoviy qism

$$-\frac{43}{85} = -0,5058823529411764$$

Yechim qadamlari

\frac{7+i}{-7+6i}ning surat va maxrajini murakkab tutash maxraj -7-6i bilan ko‘paytiring.

$$Re(\frac{\left(7+i\right)\left(-7-6i\right)}{\left(-7+6i\right)\left(-7-6i\right)})$$

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

$$Re(\frac{\left(7+i\right)\left(-7-6i\right)}{\left(-7\right)^{2}-6^{2}i^{2}})$$

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

$$Re(\frac{\left(7+i\right)\left(-7-6i\right)}{85})$$

Binomlarni ko‘paytirgandek 7+i va -7-6i murakkab sonlarni ko‘paytiring.

$$Re(\frac{7\left(-7\right)+7\times \left(-6i\right)-7i-6i^{2}}{85})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{7\left(-7\right)+7\times \left(-6i\right)-7i-6\left(-1\right)}{85})$$

7\left(-7\right)+7\times \left(-6i\right)-7i-6\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-49-42i-7i+6}{85})$$

-49-42i-7i+6 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-49+6+\left(-42-7\right)i}{85})$$

-49+6+\left(-42-7\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-43-49i}{85})$$

-\frac{43}{85}-\frac{49}{85}i ni olish uchun -43-49i ni 85 ga bo‘ling.

$$Re(-\frac{43}{85}-\frac{49}{85}i)$$

-\frac{43}{85}-\frac{49}{85}i ning real qismi – -\frac{43}{85}.

$$-\frac{43}{85}$$