Simplify (-7+3i)^2+(-2+8i)

${(- 7 + 3 i)}^{2} + (- 2 + 8 i)$

Remove parentheses.

${(- 7 + 3 i)}^{2} - 2 + 8 i$

Simplify each term.

Rewrite ${(- 7 + 3 i)}^{2}$ as $(- 7 + 3 i) (- 7 + 3 i)$ .

$(- 7 + 3 i) (- 7 + 3 i) - 2 + 8 i$

Expand $(- 7 + 3 i) (- 7 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$- 7 (- 7 + 3 i) + 3 i (- 7 + 3 i) - 2 + 8 i$

Apply the distributive property.

$- 7 \cdot - 7 - 7 (3 i) + 3 i (- 7 + 3 i) - 2 + 8 i$

Apply the distributive property.

$- 7 \cdot - 7 - 7 (3 i) + 3 i \cdot - 7 + 3 i (3 i) - 2 + 8 i$

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $- 7$ .

$49 - 7 (3 i) + 3 i \cdot - 7 + 3 i (3 i) - 2 + 8 i$

Multiply $3$ by $- 7$ .

$49 - 21 i + 3 i \cdot - 7 + 3 i (3 i) - 2 + 8 i$

Multiply $- 7$ by $3$ .

$49 - 21 i - 21 i + 3 i (3 i) - 2 + 8 i$

Multiply $3 i (3 i)$ .

Multiply $3$ by $3$ .

$49 - 21 i - 21 i + 9 i i - 2 + 8 i$

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

$49 - 21 i - 21 i + 9 (i^{1} i) - 2 + 8 i$

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

$49 - 21 i - 21 i + 9 (i^{1} i^{1}) - 2 + 8 i$

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

$49 - 21 i - 21 i + 9 i^{1 + 1} - 2 + 8 i$

Add $1$ and $1$ .

$49 - 21 i - 21 i + 9 i^{2} - 2 + 8 i$

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

$49 - 21 i - 21 i + 9 \cdot - 1 - 2 + 8 i$

Multiply $9$ by $- 1$ .

$49 - 21 i - 21 i - 9 - 2 + 8 i$

Subtract $9$ from $49$ .

$40 - 21 i - 21 i - 2 + 8 i$

Subtract $21 i$ from $- 21 i$ .

$40 - 42 i - 2 + 8 i$

Simplify by adding terms.

Subtract $2$ from $40$ .

$38 - 42 i + 8 i$

Add $- 42 i$ and $8 i$ .

$38 - 34 i$