Simplify (5+i^10)(7-i)

$(5 + i^{10}) (7 - i)$

Simplify each term.

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

Factor out $i^{8}$ .

$(5 + i^{8} i^{2}) (7 - i)$

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$(5 + {(i^{4})}^{2} i^{2}) (7 - i)$

$(5 + {(i^{4})}^{2} i^{2}) (7 - i)$

Rewrite $i^{4}$ as $1$ .

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

$(5 + {({(i^{2})}^{2})}^{2} i^{2}) (7 - i)$

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

$(5 + {({(- 1)}^{2})}^{2} i^{2}) (7 - i)$

Raise $- 1$ to the power of $2$ .

$(5 + 1^{2} i^{2}) (7 - i)$

$(5 + 1^{2} i^{2}) (7 - i)$

One to any power is one.

$(5 + 1 i^{2}) (7 - i)$

Multiply $i^{2}$ by $1$ .

$(5 + i^{2}) (7 - i)$

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

$(5 - 1) (7 - i)$

$(5 - 1) (7 - i)$

Simplify by multiplying through.

Subtract $1$ from $5$ .

$4 (7 - i)$

Apply the distributive property.

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

Multiply.

Multiply $4$ by $7$ .

$28 + 4 (- i)$

Multiply $- 1$ by $4$ .

$28 - 4 i$

$28 - 4 i$

$28 - 4 i$

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