Simplify (2/5+3/2i)^2

${(\frac{2}{5} + \frac{3}{2} i)}^{2}$

Simplify terms.

Combine $\frac{3}{2}$ and $i$ .

${(\frac{2}{5} + \frac{3 i}{2})}^{2}$

Rewrite ${(\frac{2}{5} + \frac{3 i}{2})}^{2}$ as $(\frac{2}{5} + \frac{3 i}{2}) (\frac{2}{5} + \frac{3 i}{2})$ .

$(\frac{2}{5} + \frac{3 i}{2}) (\frac{2}{5} + \frac{3 i}{2})$

Expand $(\frac{2}{5} + \frac{3 i}{2}) (\frac{2}{5} + \frac{3 i}{2})$ using the FOIL Method.

Apply the distributive property.

$\frac{2}{5} (\frac{2}{5} + \frac{3 i}{2}) + \frac{3 i}{2} (\frac{2}{5} + \frac{3 i}{2})$

Apply the distributive property.

$\frac{2}{5} \cdot \frac{2}{5} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} (\frac{2}{5} + \frac{3 i}{2})$

Apply the distributive property.

$\frac{2}{5} \cdot \frac{2}{5} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $\frac{2}{5} \cdot \frac{2}{5}$ .

Multiply $\frac{2}{5}$ by $\frac{2}{5}$ .

$\frac{2 \cdot 2}{5 \cdot 5} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Multiply $2$ by $2$ .

$\frac{4}{5 \cdot 5} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Multiply $5$ by $5$ .

$\frac{4}{25} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4}{25} + \frac{2}{5} \cdot \frac{3 i}{2} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Rewrite the expression.

$\frac{4}{25} + \frac{1}{5} (3 i) + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Combine $3$ and $\frac{1}{5}$ .

$\frac{4}{25} + \frac{3}{5} i + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Combine $\frac{3}{5}$ and $i$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{2} \cdot \frac{2}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Rewrite the expression.

$\frac{4}{25} + \frac{3 i}{5} + 3 i \frac{1}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Combine $\frac{1}{5}$ and $3$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3}{5} i + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Combine $\frac{3}{5}$ and $i$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{3 i}{2} \cdot \frac{3 i}{2}$

Multiply $\frac{3 i}{2} \cdot \frac{3 i}{2}$ .

Multiply $\frac{3 i}{2}$ by $\frac{3 i}{2}$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{3 i (3 i)}{2 \cdot 2}$

Multiply $3$ by $3$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 i i}{2 \cdot 2}$

Raise $i$ to the power of $1$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 (i^{1} i)}{2 \cdot 2}$

Raise $i$ to the power of $1$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 (i^{1} i^{1})}{2 \cdot 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 i^{1 + 1}}{2 \cdot 2}$

Add $1$ and $1$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 i^{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 i^{2}}{4}$

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

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{9 \cdot - 1}{4}$

Multiply $9$ by $- 1$ .

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} + \frac{- 9}{4}$

Move the negative in front of the fraction.

$\frac{4}{25} + \frac{3 i}{5} + \frac{3 i}{5} - \frac{9}{4}$

To write $\frac{4}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4}{25} \cdot \frac{4}{4} - \frac{9}{4} + \frac{3 i}{5} + \frac{3 i}{5}$

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{4}{25} \cdot \frac{4}{4} - \frac{9}{4} \cdot \frac{25}{25} + \frac{3 i}{5} + \frac{3 i}{5}$

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{25}$ by $\frac{4}{4}$ .

$\frac{4 \cdot 4}{25 \cdot 4} - \frac{9}{4} \cdot \frac{25}{25} + \frac{3 i}{5} + \frac{3 i}{5}$

Multiply $25$ by $4$ .

$\frac{4 \cdot 4}{100} - \frac{9}{4} \cdot \frac{25}{25} + \frac{3 i}{5} + \frac{3 i}{5}$

Multiply $\frac{9}{4}$ by $\frac{25}{25}$ .

$\frac{4 \cdot 4}{100} - \frac{9 \cdot 25}{4 \cdot 25} + \frac{3 i}{5} + \frac{3 i}{5}$

Multiply $4$ by $25$ .

$\frac{4 \cdot 4}{100} - \frac{9 \cdot 25}{100} + \frac{3 i}{5} + \frac{3 i}{5}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 9 \cdot 25}{100} + \frac{3 i}{5} + \frac{3 i}{5}$

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{16 - 9 \cdot 25}{100} + \frac{3 i}{5} + \frac{3 i}{5}$

Multiply $- 9$ by $25$ .

$\frac{16 - 225}{100} + \frac{3 i}{5} + \frac{3 i}{5}$

Subtract $225$ from $16$ .

$\frac{- 209}{100} + \frac{3 i}{5} + \frac{3 i}{5}$

Combine the numerators over the common denominator.

$\frac{- 209}{100} + \frac{6 i}{5}$

Move the negative in front of the fraction.

$- \frac{209}{100} + \frac{6 i}{5}$

Simplify (2/5+3/2i)^2

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