Simplify (7-2i)^2

${(7 - 2 i)}^{2}$

Step 1

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

$(7 - 2 i) (7 - 2 i)$

Step 2

Expand $(7 - 2 i) (7 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$7 (7 - 2 i) - 2 i (7 - 2 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $7$ .

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

Multiply $- 2$ by $7$ .

$49 - 14 i - 2 i \cdot 7 - 2 i (- 2 i)$

Multiply $7$ by $- 2$ .

$49 - 14 i - 14 i - 2 i (- 2 i)$

Multiply $- 2 i (- 2 i)$ .

Multiply $- 2$ by $- 2$ .

$49 - 14 i - 14 i + 4 i i$

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

$49 - 14 i - 14 i + 4 (i^{1} i)$

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

$49 - 14 i - 14 i + 4 (i^{1} i^{1})$

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

$49 - 14 i - 14 i + 4 i^{1 + 1}$

Add $1$ and $1$ .

$49 - 14 i - 14 i + 4 i^{2}$

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

$49 - 14 i - 14 i + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$49 - 14 i - 14 i - 4$

Subtract $4$ from $49$ .

$45 - 14 i - 14 i$

Subtract $14 i$ from $- 14 i$ .

$45 - 28 i$