Simplify ((2i)/n)^2

${(\frac{2 i}{n})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 i}{n}$ .

$\frac{{(2 i)}^{2}}{n^{2}}$

Apply the product rule to $2 i$ .

$\frac{2^{2} i^{2}}{n^{2}}$

Step 2

Simplify the numerator.

Raise $2$ to the power of $2$ .

$\frac{4 i^{2}}{n^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{4 \cdot - 1}{n^{2}}$

Step 3

Simplify the expression.

Multiply $4$ by $- 1$ .

$\frac{- 4}{n^{2}}$

Move the negative in front of the fraction.

$- \frac{4}{n^{2}}$