(3+i2)*X=(2+i4)*(2-i3) eching

$$( 3 + i 2 ) \times X = ( 2 + i 4 ) \times ( 2 - i 3 )$$

X uchun yechish

$$X=4-2i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Binomlarni ko‘paytirgandek 2+4i va 2-3i murakkab sonlarni ko‘paytiring.

$$\left(3+2i\right)X=2\times 2+2\times \left(-3i\right)+4i\times 2+4\left(-3\right)i^{2}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$\left(3+2i\right)X=2\times 2+2\times \left(-3i\right)+4i\times 2+4\left(-3\right)\left(-1\right)$$

2\times 2+2\times \left(-3i\right)+4i\times 2+4\left(-3\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\left(3+2i\right)X=4-6i+8i+12$$

4-6i+8i+12 ichida real va mavhum qismlarni birlashtiring.

$$\left(3+2i\right)X=4+12+\left(-6+8\right)i$$

4+12+\left(-6+8\right)i ichida qo‘shishlarni bajaring.

$$\left(3+2i\right)X=16+2i$$

Ikki tarafini 3+2i ga bo‘ling.

$$X=\frac{16+2i}{3+2i}$$

\frac{16+2i}{3+2i}ning surat va maxrajini murakkab tutash maxraj 3-2i bilan ko‘paytiring.

$$X=\frac{\left(16+2i\right)\left(3-2i\right)}{\left(3+2i\right)\left(3-2i\right)}$$

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

$$X=\frac{\left(16+2i\right)\left(3-2i\right)}{3^{2}-2^{2}i^{2}}$$

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

$$X=\frac{\left(16+2i\right)\left(3-2i\right)}{13}$$

Binomlarni ko‘paytirgandek 16+2i va 3-2i murakkab sonlarni ko‘paytiring.

$$X=\frac{16\times 3+16\times \left(-2i\right)+2i\times 3+2\left(-2\right)i^{2}}{13}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$X=\frac{16\times 3+16\times \left(-2i\right)+2i\times 3+2\left(-2\right)\left(-1\right)}{13}$$

16\times 3+16\times \left(-2i\right)+2i\times 3+2\left(-2\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$X=\frac{48-32i+6i+4}{13}$$

48-32i+6i+4 ichida real va mavhum qismlarni birlashtiring.

$$X=\frac{48+4+\left(-32+6\right)i}{13}$$

48+4+\left(-32+6\right)i ichida qo‘shishlarni bajaring.

$$X=\frac{52-26i}{13}$$

4-2i ni olish uchun 52-26i ni 13 ga bo‘ling.

$$X=4-2i$$