-3-2i/5+2i eching

$$\frac { - 3 - 2 i } { 5 + 2 i }$$

Baholash

$$-\frac{19}{29}-\frac{4}{29}i\approx -0,655172414-0,137931034i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 5-2i.

$$\frac{\left(-3-2i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)}$$

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

$$\frac{\left(-3-2i\right)\left(5-2i\right)}{5^{2}-2^{2}i^{2}}$$

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

$$\frac{\left(-3-2i\right)\left(5-2i\right)}{29}$$

Binomlarni ko‘paytirgandek -3-2i va 5-2i murakkab sonlarni ko‘paytiring.

$$\frac{-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)i^{2}}{29}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\frac{-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)\left(-1\right)}{29}$$

-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-15+6i-10i-4}{29}$$

-15+6i-10i-4 ichida real va mavhum qismlarni birlashtiring.

$$\frac{-15-4+\left(6-10\right)i}{29}$$

-15-4+\left(6-10\right)i ichida qo‘shishlarni bajaring.

$$\frac{-19-4i}{29}$$

-\frac{19}{29}-\frac{4}{29}i ni olish uchun -19-4i ni 29 ga bo‘ling.

$$-\frac{19}{29}-\frac{4}{29}i$$

Ashyoviy qism

$$-\frac{19}{29} = -0,6551724137931034$$

Yechim qadamlari

\frac{-3-2i}{5+2i}ning surat va maxrajini murakkab tutash maxraj 5-2i bilan ko‘paytiring.

$$Re(\frac{\left(-3-2i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)})$$

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

$$Re(\frac{\left(-3-2i\right)\left(5-2i\right)}{5^{2}-2^{2}i^{2}})$$

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

$$Re(\frac{\left(-3-2i\right)\left(5-2i\right)}{29})$$

Binomlarni ko‘paytirgandek -3-2i va 5-2i murakkab sonlarni ko‘paytiring.

$$Re(\frac{-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)i^{2}}{29})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$Re(\frac{-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)\left(-1\right)}{29})$$

-3\times 5-3\times \left(-2i\right)-2i\times 5-2\left(-2\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{-15+6i-10i-4}{29})$$

-15+6i-10i-4 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{-15-4+\left(6-10\right)i}{29})$$

-15-4+\left(6-10\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{-19-4i}{29})$$

-\frac{19}{29}-\frac{4}{29}i ni olish uchun -19-4i ni 29 ga bo‘ling.

$$Re(-\frac{19}{29}-\frac{4}{29}i)$$

-\frac{19}{29}-\frac{4}{29}i ning real qismi – -\frac{19}{29}.

$$-\frac{19}{29}$$