Simplify (2-5i)^2

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

Step 1

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

$(2 - 5 i) (2 - 5 i)$

Step 2

Expand $(2 - 5 i) (2 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$2 (2 - 5 i) - 5 i (2 - 5 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 5 i) - 5 i (2 - 5 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 5 i) - 5 i \cdot 2 - 5 i (- 5 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- 5 i) - 5 i \cdot 2 - 5 i (- 5 i)$

Multiply $- 5$ by $2$ .

$4 - 10 i - 5 i \cdot 2 - 5 i (- 5 i)$

Multiply $2$ by $- 5$ .

$4 - 10 i - 10 i - 5 i (- 5 i)$

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

Multiply $- 5$ by $- 5$ .

$4 - 10 i - 10 i + 25 i i$

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

$4 - 10 i - 10 i + 25 (i^{1} i)$

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

$4 - 10 i - 10 i + 25 (i^{1} i^{1})$

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

$4 - 10 i - 10 i + 25 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 10 i - 10 i + 25 i^{2}$

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

$4 - 10 i - 10 i + 25 \cdot - 1$

Multiply $25$ by $- 1$ .

$4 - 10 i - 10 i - 25$

Subtract $25$ from $4$ .

$- 21 - 10 i - 10 i$

Subtract $10 i$ from $- 10 i$ .

$- 21 - 20 i$