Simplify (1-5i)^2

${(1 - 5 i)}^{2}$

Step 1

Rewrite ${(1 - 5 i)}^{2}$ as $(1 - 5 i) (1 - 5 i)$ .

$(1 - 5 i) (1 - 5 i)$

Step 2

Expand $(1 - 5 i) (1 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$1 (1 - 5 i) - 5 i (1 - 5 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 5 i) - 5 i (1 - 5 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 5 i) - 5 i \cdot 1 - 5 i (- 5 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (- 5 i) - 5 i \cdot 1 - 5 i (- 5 i)$

Multiply $- 5 i$ by $1$ .

$1 - 5 i - 5 i \cdot 1 - 5 i (- 5 i)$

Multiply $- 5$ by $1$ .

$1 - 5 i - 5 i - 5 i (- 5 i)$

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

Multiply $- 5$ by $- 5$ .

$1 - 5 i - 5 i + 25 i i$

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

$1 - 5 i - 5 i + 25 (i^{1} i)$

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

$1 - 5 i - 5 i + 25 (i^{1} i^{1})$

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

$1 - 5 i - 5 i + 25 i^{1 + 1}$

Add $1$ and $1$ .

$1 - 5 i - 5 i + 25 i^{2}$

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

$1 - 5 i - 5 i + 25 \cdot - 1$

Multiply $25$ by $- 1$ .

$1 - 5 i - 5 i - 25$

Subtract $25$ from $1$ .

$- 24 - 5 i - 5 i$

Subtract $5 i$ from $- 5 i$ .

$- 24 - 10 i$