Solve (-frac{2sqrt{2}i}{2x})^2

$$( - \frac { 2 \sqrt { 2 } i } { 2 x } ) ^ { 2 }$$

Evaluate

$$-\frac{2}{x^{2}}$$

Solution Steps

Calculate -\frac{2i\sqrt{2}}{2x} to the power of 2 and get \left(\frac{2i\sqrt{2}}{2x}\right)^{2}.

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

To raise \frac{2i\sqrt{2}}{2x} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2i\sqrt{2}\right)^{2}.

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

Calculate 2i to the power of 2 and get -4.

$$\frac{-4\left(\sqrt{2}\right)^{2}}{\left(2x\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-4\times 2}{\left(2x\right)^{2}}$$

Multiply -4 and 2 to get -8.

$$\frac{-8}{\left(2x\right)^{2}}$$

Expand \left(2x\right)^{2}.

$$\frac{-8}{2^{2}x^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-8}{4x^{2}}$$

Expand

$$-\frac{2}{x^{2}}$$

Solution Steps

Calculate -\frac{2i\sqrt{2}}{2x} to the power of 2 and get \left(\frac{2i\sqrt{2}}{2x}\right)^{2}.

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

To raise \frac{2i\sqrt{2}}{2x} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2i\sqrt{2}\right)^{2}.

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

Calculate 2i to the power of 2 and get -4.

$$\frac{-4\left(\sqrt{2}\right)^{2}}{\left(2x\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-4\times 2}{\left(2x\right)^{2}}$$

Multiply -4 and 2 to get -8.

$$\frac{-8}{\left(2x\right)^{2}}$$

Expand \left(2x\right)^{2}.

$$\frac{-8}{2^{2}x^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-8}{4x^{2}}$$