Simplify (2-7i)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- 7 i) - 7 i \cdot 2 - 7 i (- 7 i)$

Multiply $- 7$ by $2$ .

$4 - 14 i - 7 i \cdot 2 - 7 i (- 7 i)$

Multiply $2$ by $- 7$ .

$4 - 14 i - 14 i - 7 i (- 7 i)$

Multiply $- 7 i (- 7 i)$ .

Multiply $- 7$ by $- 7$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $49$ by $- 1$ .

$4 - 14 i - 14 i - 49$

Subtract $49$ from $4$ .

$- 45 - 14 i - 14 i$

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

$- 45 - 28 i$