Simplify (1-7i)^2

${(1 - 7 i)}^{2}$

Rewrite ${(1 - 7 i)}^{2}$ as $(1 - 7 i) (1 - 7 i)$ .

$(1 - 7 i) (1 - 7 i)$

Expand $(1 - 7 i) (1 - 7 i)$ using the FOIL Method.

Apply the distributive property.

$1 (1 - 7 i) - 7 i (1 - 7 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 7 i) - 7 i (1 - 7 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 7 i) - 7 i \cdot 1 - 7 i (- 7 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (- 7 i) - 7 i \cdot 1 - 7 i (- 7 i)$

Multiply $- 7 i$ by $1$ .

$1 - 7 i - 7 i \cdot 1 - 7 i (- 7 i)$

Multiply $- 7$ by $1$ .

$1 - 7 i - 7 i - 7 i (- 7 i)$

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

Multiply $- 7$ by $- 7$ .

$1 - 7 i - 7 i + 49 i i$

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

$1 - 7 i - 7 i + 49 (i^{1} i)$

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

$1 - 7 i - 7 i + 49 (i^{1} i^{1})$

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

$1 - 7 i - 7 i + 49 i^{1 + 1}$

Add $1$ and $1$ .

$1 - 7 i - 7 i + 49 i^{2}$

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

$1 - 7 i - 7 i + 49 \cdot - 1$

Multiply $49$ by $- 1$ .

$1 - 7 i - 7 i - 49$

Subtract $49$ from $1$ .

$- 48 - 7 i - 7 i$

Subtract $7 i$ from $- 7 i$ .

$- 48 - 14 i$