Simplify (1-5i)^2-(8-4i)

${(1 - 5 i)}^{2} - (8 - 4 i)$

Simplify each term.

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

$(1 - 5 i) (1 - 5 i) - (8 - 4 i)$

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

Apply the distributive property.

$1 (1 - 5 i) - 5 i (1 - 5 i) - (8 - 4 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 5 i) - 5 i (1 - 5 i) - (8 - 4 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- 5 i) - 5 i \cdot 1 - 5 i (- 5 i) - (8 - 4 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (- 5 i) - 5 i \cdot 1 - 5 i (- 5 i) - (8 - 4 i)$

Multiply $- 5 i$ by $1$ .

$1 - 5 i - 5 i \cdot 1 - 5 i (- 5 i) - (8 - 4 i)$

Multiply $- 5$ by $1$ .

$1 - 5 i - 5 i - 5 i (- 5 i) - (8 - 4 i)$

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

Multiply $- 5$ by $- 5$ .

$1 - 5 i - 5 i + 25 i i - (8 - 4 i)$

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

$1 - 5 i - 5 i + 25 (i^{1} i) - (8 - 4 i)$

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

$1 - 5 i - 5 i + 25 (i^{1} i^{1}) - (8 - 4 i)$

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

$1 - 5 i - 5 i + 25 i^{1 + 1} - (8 - 4 i)$

Add $1$ and $1$ .

$1 - 5 i - 5 i + 25 i^{2} - (8 - 4 i)$

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

$1 - 5 i - 5 i + 25 \cdot - 1 - (8 - 4 i)$

Multiply $25$ by $- 1$ .

$1 - 5 i - 5 i - 25 - (8 - 4 i)$

Subtract $25$ from $1$ .

$- 24 - 5 i - 5 i - (8 - 4 i)$

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

$- 24 - 10 i - (8 - 4 i)$

Apply the distributive property.

$- 24 - 10 i - 1 \cdot 8 - (- 4 i)$

Multiply $- 1$ by $8$ .

$- 24 - 10 i - 8 - (- 4 i)$

Multiply $- 4$ by $- 1$ .

$- 24 - 10 i - 8 + 4 i$

Simplify by adding terms.

Subtract $8$ from $- 24$ .

$- 32 - 10 i + 4 i$

Add $- 10 i$ and $4 i$ .

$- 32 - 6 i$

Simplify (1-5i)^2-(8-4i)

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