Simplify 8i^119+i^78-3i^97+9i^44

$8 i^{119} + i^{78} - 3 i^{97} + 9 i^{44}$

Step 1

Simplify each term.

Rewrite $i^{119}$ as ${(i^{4})}^{29} (i^{2} \cdot i)$ .

Factor out $i^{116}$ .

$8 (i^{116} i^{3}) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 ({(i^{4})}^{29} i^{3}) + i^{78} - 3 i^{97} + 9 i^{44}$

Factor out $i^{2}$ .

$8 ({(i^{4})}^{29} (i^{2} \cdot i)) + i^{78} - 3 i^{97} + 9 i^{44}$

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

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

$8 ({({(i^{2})}^{2})}^{29} (i^{2} \cdot i)) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 ({({(- 1)}^{2})}^{29} (i^{2} \cdot i)) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 (1^{29} (i^{2} \cdot i)) + i^{78} - 3 i^{97} + 9 i^{44}$

One to any power is one.

$8 (1 (i^{2} \cdot i)) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 (i^{2} \cdot i) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 (- 1 \cdot i) + i^{78} - 3 i^{97} + 9 i^{44}$

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

$8 (- i) + i^{78} - 3 i^{97} + 9 i^{44}$

Multiply $- 1$ by $8$ .

$- 8 i + i^{78} - 3 i^{97} + 9 i^{44}$

Rewrite $i^{78}$ as ${(i^{4})}^{19} i^{2}$ .

Factor out $i^{76}$ .

$- 8 i + i^{76} i^{2} - 3 i^{97} + 9 i^{44}$

Rewrite $i^{76}$ as ${(i^{4})}^{19}$ .

$- 8 i + {(i^{4})}^{19} i^{2} - 3 i^{97} + 9 i^{44}$

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

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

$- 8 i + {({(i^{2})}^{2})}^{19} i^{2} - 3 i^{97} + 9 i^{44}$

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

$- 8 i + {({(- 1)}^{2})}^{19} i^{2} - 3 i^{97} + 9 i^{44}$

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

$- 8 i + 1^{19} i^{2} - 3 i^{97} + 9 i^{44}$

One to any power is one.

$- 8 i + 1 i^{2} - 3 i^{97} + 9 i^{44}$

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

$- 8 i + i^{2} - 3 i^{97} + 9 i^{44}$

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

$- 8 i - 1 - 3 i^{97} + 9 i^{44}$

Rewrite $i^{97}$ as ${(i^{4})}^{24} i$ .

Factor out $i^{96}$ .

$- 8 i - 1 - 3 (i^{96} i) + 9 i^{44}$

Rewrite $i^{96}$ as ${(i^{4})}^{24}$ .

$- 8 i - 1 - 3 ({(i^{4})}^{24} i) + 9 i^{44}$

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

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

$- 8 i - 1 - 3 ({({(i^{2})}^{2})}^{24} i) + 9 i^{44}$

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

$- 8 i - 1 - 3 ({({(- 1)}^{2})}^{24} i) + 9 i^{44}$

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

$- 8 i - 1 - 3 (1^{24} i) + 9 i^{44}$

One to any power is one.

$- 8 i - 1 - 3 (1 i) + 9 i^{44}$

Multiply $i$ by $1$ .

$- 8 i - 1 - 3 i + 9 i^{44}$

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

$- 8 i - 1 - 3 i + 9 {(i^{4})}^{11}$

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

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

$- 8 i - 1 - 3 i + 9 {({(i^{2})}^{2})}^{11}$

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

$- 8 i - 1 - 3 i + 9 {({(- 1)}^{2})}^{11}$

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

$- 8 i - 1 - 3 i + 9 \cdot 1^{11}$

One to any power is one.

$- 8 i - 1 - 3 i + 9 \cdot 1$

Multiply $9$ by $1$ .

$- 8 i - 1 - 3 i + 9$

Step 2

Simplify by adding terms.

Subtract $3 i$ from $- 8 i$ .

$- 1 - 11 i + 9$

Add $- 1$ and $9$ .

$8 - 11 i$

Simplify 8i^119+i^78-3i^97+9i^44

Related Questions

Support LCMGCF.com by disabling your adblocker.