Simplify (2-6i)^2

${(2 - 6 i)}^{2}$

Step 1

Rewrite ${(2 - 6 i)}^{2}$ as $(2 - 6 i) (2 - 6 i)$ .

$(2 - 6 i) (2 - 6 i)$

Step 2

Expand $(2 - 6 i) (2 - 6 i)$ using the FOIL Method.

Apply the distributive property.

$2 (2 - 6 i) - 6 i (2 - 6 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 6 i) - 6 i (2 - 6 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 6 i) - 6 i \cdot 2 - 6 i (- 6 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- 6 i) - 6 i \cdot 2 - 6 i (- 6 i)$

Multiply $- 6$ by $2$ .

$4 - 12 i - 6 i \cdot 2 - 6 i (- 6 i)$

Multiply $2$ by $- 6$ .

$4 - 12 i - 12 i - 6 i (- 6 i)$

Multiply $- 6 i (- 6 i)$ .

Multiply $- 6$ by $- 6$ .

$4 - 12 i - 12 i + 36 i i$

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

$4 - 12 i - 12 i + 36 (i^{1} i)$

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

$4 - 12 i - 12 i + 36 (i^{1} i^{1})$

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

$4 - 12 i - 12 i + 36 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 12 i - 12 i + 36 i^{2}$

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

$4 - 12 i - 12 i + 36 \cdot - 1$

Multiply $36$ by $- 1$ .

$4 - 12 i - 12 i - 36$

Subtract $36$ from $4$ .

$- 32 - 12 i - 12 i$

Subtract $12 i$ from $- 12 i$ .

$- 32 - 24 i$