Simplify 11i^59+6i^12+9i^15+i^11

$11 i^{59} + 6 i^{12} + 9 i^{15} + i^{11}$

Simplify each term.

Rewrite $i^{59}$ as ${(i^{4})}^{14} (i^{2} \cdot i)$ .

Factor out $i^{56}$ .

$11 (i^{56} i^{3}) + 6 i^{12} + 9 i^{15} + i^{11}$

Rewrite $i^{56}$ as ${(i^{4})}^{14}$ .

$11 ({(i^{4})}^{14} i^{3}) + 6 i^{12} + 9 i^{15} + i^{11}$

Factor out $i^{2}$ .

$11 ({(i^{4})}^{14} (i^{2} \cdot i)) + 6 i^{12} + 9 i^{15} + i^{11}$

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

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

$11 ({({(i^{2})}^{2})}^{14} (i^{2} \cdot i)) + 6 i^{12} + 9 i^{15} + i^{11}$

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

$11 ({({(- 1)}^{2})}^{14} (i^{2} \cdot i)) + 6 i^{12} + 9 i^{15} + i^{11}$

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

$11 (1^{14} (i^{2} \cdot i)) + 6 i^{12} + 9 i^{15} + i^{11}$

One to any power is one.

$11 (1 (i^{2} \cdot i)) + 6 i^{12} + 9 i^{15} + i^{11}$

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

$11 (i^{2} \cdot i) + 6 i^{12} + 9 i^{15} + i^{11}$

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

$11 (- 1 \cdot i) + 6 i^{12} + 9 i^{15} + i^{11}$

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

$11 (- i) + 6 i^{12} + 9 i^{15} + i^{11}$

Multiply $- 1$ by $11$ .

$- 11 i + 6 i^{12} + 9 i^{15} + i^{11}$

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$- 11 i + 6 {(i^{4})}^{3} + 9 i^{15} + i^{11}$

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

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

$- 11 i + 6 {({(i^{2})}^{2})}^{3} + 9 i^{15} + i^{11}$

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

$- 11 i + 6 {({(- 1)}^{2})}^{3} + 9 i^{15} + i^{11}$

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

$- 11 i + 6 \cdot 1^{3} + 9 i^{15} + i^{11}$

One to any power is one.

$- 11 i + 6 \cdot 1 + 9 i^{15} + i^{11}$

Multiply $6$ by $1$ .

$- 11 i + 6 + 9 i^{15} + i^{11}$

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

Factor out $i^{12}$ .

$- 11 i + 6 + 9 (i^{12} i^{3}) + i^{11}$

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$- 11 i + 6 + 9 ({(i^{4})}^{3} i^{3}) + i^{11}$

Factor out $i^{2}$ .

$- 11 i + 6 + 9 ({(i^{4})}^{3} (i^{2} \cdot i)) + i^{11}$

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

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

$- 11 i + 6 + 9 ({({(i^{2})}^{2})}^{3} (i^{2} \cdot i)) + i^{11}$

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

$- 11 i + 6 + 9 ({({(- 1)}^{2})}^{3} (i^{2} \cdot i)) + i^{11}$

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

$- 11 i + 6 + 9 (1^{3} (i^{2} \cdot i)) + i^{11}$

One to any power is one.

$- 11 i + 6 + 9 (1 (i^{2} \cdot i)) + i^{11}$

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

$- 11 i + 6 + 9 (i^{2} \cdot i) + i^{11}$

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

$- 11 i + 6 + 9 (- 1 \cdot i) + i^{11}$

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

$- 11 i + 6 + 9 (- i) + i^{11}$

Multiply $- 1$ by $9$ .

$- 11 i + 6 - 9 i + i^{11}$

Rewrite $i^{11}$ as ${(i^{4})}^{2} (i^{2} \cdot i)$ .

Factor out $i^{8}$ .

$- 11 i + 6 - 9 i + i^{8} i^{3}$

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

$- 11 i + 6 - 9 i + {(i^{4})}^{2} i^{3}$

Factor out $i^{2}$ .

$- 11 i + 6 - 9 i + {(i^{4})}^{2} (i^{2} \cdot i)$

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

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

$- 11 i + 6 - 9 i + {({(i^{2})}^{2})}^{2} (i^{2} \cdot i)$

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

$- 11 i + 6 - 9 i + {({(- 1)}^{2})}^{2} (i^{2} \cdot i)$

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

$- 11 i + 6 - 9 i + 1^{2} (i^{2} \cdot i)$

One to any power is one.

$- 11 i + 6 - 9 i + 1 (i^{2} \cdot i)$

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

$- 11 i + 6 - 9 i + i^{2} \cdot i$

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

$- 11 i + 6 - 9 i - 1 \cdot i$

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

$- 11 i + 6 - 9 i - i$

Simplify by adding terms.

Subtract $9 i$ from $- 11 i$ .

$6 - 20 i - i$

Subtract $i$ from $- 20 i$ .

$6 - 21 i$

Simplify 11i^59+6i^12+9i^15+i^11

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