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

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

Simplify each term.

Factor out $i^{2}$ .

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

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

$(2 - 3 (- 1 \cdot i)) (1 + i)$

Rewrite $- 1 i$ as $- i$ .

$(2 - 3 (- i)) (1 + i)$

Multiply $- 1$ by $- 3$ .

$(2 + 3 i) (1 + i)$

$(2 + 3 i) (1 + i)$

Expand $(2 + 3 i) (1 + i)$ using the FOIL Method.

Apply the distributive property.

$2 (1 + i) + 3 i (1 + i)$

Apply the distributive property.

$2 \cdot 1 + 2 i + 3 i (1 + i)$

Apply the distributive property.

$2 \cdot 1 + 2 i + 3 i \cdot 1 + 3 i i$

$2 \cdot 1 + 2 i + 3 i \cdot 1 + 3 i i$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $1$ .

$2 + 2 i + 3 i \cdot 1 + 3 i i$

Multiply $3$ by $1$ .

$2 + 2 i + 3 i + 3 i i$

Multiply $3 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

$2 + 2 i + 3 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$2 + 2 i + 3 i - 3$

$2 + 2 i + 3 i - 3$

Subtract $3$ from $2$ .

$- 1 + 2 i + 3 i$

Add $2 i$ and $3 i$ .

$- 1 + 5 i$

$- 1 + 5 i$

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