Simplify (4-8i)^2

${(4 - 8 i)}^{2}$

Step 1

Rewrite ${(4 - 8 i)}^{2}$ as $(4 - 8 i) (4 - 8 i)$ .

$(4 - 8 i) (4 - 8 i)$

Step 2

Expand $(4 - 8 i) (4 - 8 i)$ using the FOIL Method.

Apply the distributive property.

$4 (4 - 8 i) - 8 i (4 - 8 i)$

Apply the distributive property.

$4 \cdot 4 + 4 (- 8 i) - 8 i (4 - 8 i)$

Apply the distributive property.

$4 \cdot 4 + 4 (- 8 i) - 8 i \cdot 4 - 8 i (- 8 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- 8 i) - 8 i \cdot 4 - 8 i (- 8 i)$

Multiply $- 8$ by $4$ .

$16 - 32 i - 8 i \cdot 4 - 8 i (- 8 i)$

Multiply $4$ by $- 8$ .

$16 - 32 i - 32 i - 8 i (- 8 i)$

Multiply $- 8 i (- 8 i)$ .

Multiply $- 8$ by $- 8$ .

$16 - 32 i - 32 i + 64 i i$

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

$16 - 32 i - 32 i + 64 (i^{1} i)$

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

$16 - 32 i - 32 i + 64 (i^{1} i^{1})$

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

$16 - 32 i - 32 i + 64 i^{1 + 1}$

Add $1$ and $1$ .

$16 - 32 i - 32 i + 64 i^{2}$

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

$16 - 32 i - 32 i + 64 \cdot - 1$

Multiply $64$ by $- 1$ .

$16 - 32 i - 32 i - 64$

Subtract $64$ from $16$ .

$- 48 - 32 i - 32 i$

Subtract $32 i$ from $- 32 i$ .

$- 48 - 64 i$