6i/7-3i eching

$$\frac { 6 i } { 7 - 3 i }$$

Baholash

$$-\frac{9}{29}+\frac{21}{29}i\approx -0,310344828+0,724137931i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 7+3i.

$$\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)}$$

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

$$\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}}$$

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

$$\frac{6i\left(7+3i\right)}{58}$$

6i ni 7+3i marotabaga ko'paytirish.

$$\frac{6i\times 7+6\times 3i^{2}}{58}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{6i\times 7+6\times 3\left(-1\right)}{58}$$

6i\times 7+6\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

$$\frac{-18+42i}{58}$$

-\frac{9}{29}+\frac{21}{29}i ni olish uchun -18+42i ni 58 ga bo‘ling.

$$-\frac{9}{29}+\frac{21}{29}i$$

Ashyoviy qism

$$-\frac{9}{29} = -0,3103448275862069$$

Yechim qadamlari

\frac{6i}{7-3i}ning surat va maxrajini murakkab tutash maxraj 7+3i bilan ko‘paytiring.

$$Re(\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)})$$

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

$$Re(\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{6i\left(7+3i\right)}{58})$$

6i ni 7+3i marotabaga ko'paytirish.

$$Re(\frac{6i\times 7+6\times 3i^{2}}{58})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{6i\times 7+6\times 3\left(-1\right)}{58})$$

6i\times 7+6\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

$$Re(\frac{-18+42i}{58})$$

-\frac{9}{29}+\frac{21}{29}i ni olish uchun -18+42i ni 58 ga bo‘ling.

$$Re(-\frac{9}{29}+\frac{21}{29}i)$$

-\frac{9}{29}+\frac{21}{29}i ning real qismi – -\frac{9}{29}.

$$-\frac{9}{29}$$