frac{isqrt{2}-5}{i+sqrt{2}} eching

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

Baholash

$$-\frac{4\sqrt{2}}{3}+\frac{7}{3}i\approx -1,885618083+2,333333333i$$

Yechim qadamlari

\frac{i\sqrt{2}-5}{i+\sqrt{2}} maxrajini i-\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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

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

i kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

$$\frac{\left(i\sqrt{2}-5\right)\left(i-\sqrt{2}\right)}{-1-2}$$

-3 olish uchun -1 dan 2 ni ayirish.

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

i\sqrt{2}-5 ifodaning har bir elementini i-\sqrt{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

\sqrt{2} kvadrati – 2.

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

-2i hosil qilish uchun -i va 2 ni ko'paytirish.

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

-7i olish uchun -2i dan 5i ni ayirish.

$$\frac{-\sqrt{2}-7i+5\sqrt{2}}{-3}$$

4\sqrt{2} ni olish uchun -\sqrt{2} va 5\sqrt{2} ni birlashtirish.

$$\frac{4\sqrt{2}-7i}{-3}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-4\sqrt{2}+7i}{3}$$

Ashyoviy qism

$$-\frac{4 \sqrt{2}}{3} = -1,885618083164127$$