Simplify (8-5i)^2

${(8 - 5 i)}^{2}$

Step 1

Rewrite ${(8 - 5 i)}^{2}$ as $(8 - 5 i) (8 - 5 i)$ .

$(8 - 5 i) (8 - 5 i)$

Step 2

Expand $(8 - 5 i) (8 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$8 (8 - 5 i) - 5 i (8 - 5 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 5 i) - 5 i (8 - 5 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 5 i) - 5 i \cdot 8 - 5 i (- 5 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 (- 5 i) - 5 i \cdot 8 - 5 i (- 5 i)$

Multiply $- 5$ by $8$ .

$64 - 40 i - 5 i \cdot 8 - 5 i (- 5 i)$

Multiply $8$ by $- 5$ .

$64 - 40 i - 40 i - 5 i (- 5 i)$

Multiply $- 5 i (- 5 i)$ .

Multiply $- 5$ by $- 5$ .

$64 - 40 i - 40 i + 25 i i$

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

$64 - 40 i - 40 i + 25 (i^{1} i)$

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

$64 - 40 i - 40 i + 25 (i^{1} i^{1})$

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

$64 - 40 i - 40 i + 25 i^{1 + 1}$

Add $1$ and $1$ .

$64 - 40 i - 40 i + 25 i^{2}$

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

$64 - 40 i - 40 i + 25 \cdot - 1$

Multiply $25$ by $- 1$ .

$64 - 40 i - 40 i - 25$

Subtract $25$ from $64$ .

$39 - 40 i - 40 i$

Subtract $40 i$ from $- 40 i$ .

$39 - 80 i$