Simplify -2i^19-10i^116-10i^17+i^85

$- 2 i^{19} - 10 i^{116} - 10 i^{17} + i^{85}$

Simplify each term.

Rewrite $i^{19}$ as ${(i^{4})}^{4} (i^{2} \cdot i)$ .

Factor out $i^{16}$ .

$- 2 (i^{16} i^{3}) - 10 i^{116} - 10 i^{17} + i^{85}$

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$- 2 ({(i^{4})}^{4} i^{3}) - 10 i^{116} - 10 i^{17} + i^{85}$

Factor out $i^{2}$ .

$- 2 ({(i^{4})}^{4} (i^{2} \cdot i)) - 10 i^{116} - 10 i^{17} + i^{85}$

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

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

$- 2 ({({(i^{2})}^{2})}^{4} (i^{2} \cdot i)) - 10 i^{116} - 10 i^{17} + i^{85}$

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

$- 2 ({({(- 1)}^{2})}^{4} (i^{2} \cdot i)) - 10 i^{116} - 10 i^{17} + i^{85}$

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

$- 2 (1^{4} (i^{2} \cdot i)) - 10 i^{116} - 10 i^{17} + i^{85}$

One to any power is one.

$- 2 (1 (i^{2} \cdot i)) - 10 i^{116} - 10 i^{17} + i^{85}$

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

$- 2 (i^{2} \cdot i) - 10 i^{116} - 10 i^{17} + i^{85}$

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

$- 2 (- 1 \cdot i) - 10 i^{116} - 10 i^{17} + i^{85}$

Rewrite $- 1 i$ as $- i$ .

$- 2 (- i) - 10 i^{116} - 10 i^{17} + i^{85}$

Multiply $- 1$ by $- 2$ .

$2 i - 10 i^{116} - 10 i^{17} + i^{85}$

Rewrite $i^{116}$ as ${(i^{4})}^{29}$ .

$2 i - 10 {(i^{4})}^{29} - 10 i^{17} + i^{85}$

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

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

$2 i - 10 {({(i^{2})}^{2})}^{29} - 10 i^{17} + i^{85}$

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

$2 i - 10 {({(- 1)}^{2})}^{29} - 10 i^{17} + i^{85}$

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

$2 i - 10 \cdot 1^{29} - 10 i^{17} + i^{85}$

One to any power is one.

$2 i - 10 \cdot 1 - 10 i^{17} + i^{85}$

Multiply $- 10$ by $1$ .

$2 i - 10 - 10 i^{17} + i^{85}$

Rewrite $i^{17}$ as ${(i^{4})}^{4} i$ .

Factor out $i^{16}$ .

$2 i - 10 - 10 (i^{16} i) + i^{85}$

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$2 i - 10 - 10 ({(i^{4})}^{4} i) + i^{85}$

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

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

$2 i - 10 - 10 ({({(i^{2})}^{2})}^{4} i) + i^{85}$

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

$2 i - 10 - 10 ({({(- 1)}^{2})}^{4} i) + i^{85}$

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

$2 i - 10 - 10 (1^{4} i) + i^{85}$

One to any power is one.

$2 i - 10 - 10 (1 i) + i^{85}$

Multiply $i$ by $1$ .

$2 i - 10 - 10 i + i^{85}$

Rewrite $i^{85}$ as ${(i^{4})}^{21} i$ .

Factor out $i^{84}$ .

$2 i - 10 - 10 i + i^{84} i$

Rewrite $i^{84}$ as ${(i^{4})}^{21}$ .

$2 i - 10 - 10 i + {(i^{4})}^{21} i$

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

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

$2 i - 10 - 10 i + {({(i^{2})}^{2})}^{21} i$

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

$2 i - 10 - 10 i + {({(- 1)}^{2})}^{21} i$

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

$2 i - 10 - 10 i + 1^{21} i$

One to any power is one.

$2 i - 10 - 10 i + 1 i$

Multiply $i$ by $1$ .

$2 i - 10 - 10 i + i$

Simplify by adding terms.

Subtract $10 i$ from $2 i$ .

$- 10 - 8 i + i$

Add $- 8 i$ and $i$ .

$- 10 - 7 i$

Simplify -2i^19-10i^116-10i^17+i^85

Related Questions

Support LCMGCF.com by disabling your adblocker.