1+i/3-2i eching

$$\frac { 1 + i } { 3 - 2 i }$$

Baholash

$$\frac{1}{13}+\frac{5}{13}i\approx 0,076923077+0,384615385i$$

Yechim qadamlari

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 3+2i.

$$\frac{\left(1+i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}$$

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

$$\frac{\left(1+i\right)\left(3+2i\right)}{3^{2}-2^{2}i^{2}}$$

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

$$\frac{\left(1+i\right)\left(3+2i\right)}{13}$$

Binomlarni ko‘paytirgandek 1+i va 3+2i murakkab sonlarni ko‘paytiring.

$$\frac{1\times 3+1\times \left(2i\right)+3i+2i^{2}}{13}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$\frac{3+2i+3i-2}{13}$$

3+2i+3i-2 ichida real va mavhum qismlarni birlashtiring.

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

3-2+\left(2+3\right)i ichida qo‘shishlarni bajaring.

$$\frac{1+5i}{13}$$

\frac{1}{13}+\frac{5}{13}i ni olish uchun 1+5i ni 13 ga bo‘ling.

$$\frac{1}{13}+\frac{5}{13}i$$

Ashyoviy qism

$$\frac{1}{13} = 0,07692307692307693$$

Yechim qadamlari

\frac{1+i}{3-2i}ning surat va maxrajini murakkab tutash maxraj 3+2i bilan ko‘paytiring.

$$Re(\frac{\left(1+i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)})$$

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

$$Re(\frac{\left(1+i\right)\left(3+2i\right)}{3^{2}-2^{2}i^{2}})$$

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

$$Re(\frac{\left(1+i\right)\left(3+2i\right)}{13})$$

Binomlarni ko‘paytirgandek 1+i va 3+2i murakkab sonlarni ko‘paytiring.

$$Re(\frac{1\times 3+1\times \left(2i\right)+3i+2i^{2}}{13})$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

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

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

$$Re(\frac{3+2i+3i-2}{13})$$

3+2i+3i-2 ichida real va mavhum qismlarni birlashtiring.

$$Re(\frac{3-2+\left(2+3\right)i}{13})$$

3-2+\left(2+3\right)i ichida qo‘shishlarni bajaring.

$$Re(\frac{1+5i}{13})$$

\frac{1}{13}+\frac{5}{13}i ni olish uchun 1+5i ni 13 ga bo‘ling.

$$Re(\frac{1}{13}+\frac{5}{13}i)$$

\frac{1}{13}+\frac{5}{13}i ning real qismi – \frac{1}{13}.

$$\frac{1}{13}$$