(-1/2+1/2isqrt{3})^2 eching

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

Baholash

$$\frac{-\sqrt{3}i-1}{2}\approx -0,5-0,866025404i$$

Yechim qadamlari

\frac{-1}{2} kasri manfiy belgini olib tashlash bilan -\frac{1}{2} sifatida qayta yozilishi mumkin.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-\frac{1}{2}+\frac{1}{2}i\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{1}{4}\times 3$$

-\frac{3}{4} hosil qilish uchun -\frac{1}{4} va 3 ni ko'paytirish.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{3}{4}$$

-\frac{1}{2} olish uchun \frac{1}{4} dan \frac{3}{4} ni ayirish.

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

Kengaytirish

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

Yechim qadamlari

\frac{-1}{2} kasri manfiy belgini olib tashlash bilan -\frac{1}{2} sifatida qayta yozilishi mumkin.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-\frac{1}{2}+\frac{1}{2}i\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{1}{4}\times 3$$

-\frac{3}{4} hosil qilish uchun -\frac{1}{4} va 3 ni ko'paytirish.

$$\frac{1}{4}-\frac{1}{2}i\sqrt{3}-\frac{3}{4}$$

-\frac{1}{2} olish uchun \frac{1}{4} dan \frac{3}{4} ni ayirish.

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