Simplify (3+2i)/((1+i)^2)

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

Rewrite ${(1 + i)}^{2}$ as $(1 + i) (1 + i)$ .

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

Expand $(1 + i) (1 + i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$\frac{3 + 2 i}{1 \cdot 1 + 1 i + i \cdot 1 + i i}$

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$\frac{3 + 2 i}{1 + 1 i + i \cdot 1 + i i}$

Multiply $i$ by $1$ .

$\frac{3 + 2 i}{1 + i + i \cdot 1 + i i}$

Multiply $i$ by $1$ .

$\frac{3 + 2 i}{1 + i + i + i i}$

Multiply $i i$ .

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

$\frac{3 + 2 i}{1 + i + i + i^{1} i}$

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

$\frac{3 + 2 i}{1 + i + i + i^{1} i^{1}}$

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

$\frac{3 + 2 i}{1 + i + i + i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 + 2 i}{1 + i + i + i^{2}}$

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

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

Subtract $1$ from $1$ .

$\frac{3 + 2 i}{0 + i + i}$

Add $0$ and $i$ .

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

Add $i$ and $i$ .

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

Multiply the numerator and denominator of $\frac{3 + 2 i}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

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

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2 i i$ .

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

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

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

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

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

$\frac{3 i + 2 i^{1 + 1}}{2 i i}$

Add $1$ and $1$ .

$\frac{3 i + 2 i^{2}}{2 i i}$

Simplify each term.

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

$\frac{3 i + 2 \cdot - 1}{2 i i}$

Multiply $2$ by $- 1$ .

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

Reorder $3 i$ and $- 2$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{- 2 + 3 i}{2 i^{2}}$

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

$\frac{- 2 + 3 i}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

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

Split the fraction $\frac{- 2 + 3 i}{- 2}$ into two fractions.

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

Simplify each term.

Divide $- 2$ by $- 2$ .

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

Move the negative in front of the fraction.

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

Simplify (3+2i)/((1+i)^2)

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