Simplify (4-7i)^2

${(4 - 7 i)}^{2}$

Step 1

Rewrite ${(4 - 7 i)}^{2}$ as $(4 - 7 i) (4 - 7 i)$ .

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

Step 2

Expand $(4 - 7 i) (4 - 7 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- 7 i) - 7 i \cdot 4 - 7 i (- 7 i)$

Multiply $- 7$ by $4$ .

$16 - 28 i - 7 i \cdot 4 - 7 i (- 7 i)$

Multiply $4$ by $- 7$ .

$16 - 28 i - 28 i - 7 i (- 7 i)$

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

Multiply $- 7$ by $- 7$ .

$16 - 28 i - 28 i + 49 i i$

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

$16 - 28 i - 28 i + 49 (i^{1} i)$

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

$16 - 28 i - 28 i + 49 (i^{1} i^{1})$

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

$16 - 28 i - 28 i + 49 i^{1 + 1}$

Add $1$ and $1$ .

$16 - 28 i - 28 i + 49 i^{2}$

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

$16 - 28 i - 28 i + 49 \cdot - 1$

Multiply $49$ by $- 1$ .

$16 - 28 i - 28 i - 49$

Subtract $49$ from $16$ .

$- 33 - 28 i - 28 i$

Subtract $28 i$ from $- 28 i$ .

$- 33 - 56 i$