Simplify (11i^4+4i^3)-(2i^4-6i^3)

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

Simplify each term.

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

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

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

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

$11 {(- 1)}^{2} + 4 i^{3} - (2 i^{4} - 6 i^{3})$

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

$11 \cdot 1 + 4 i^{3} - (2 i^{4} - 6 i^{3})$

$11 \cdot 1 + 4 i^{3} - (2 i^{4} - 6 i^{3})$

Multiply $11$ by $1$ .

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

Factor out $i^{2}$ .

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

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

$11 + 4 (- 1 \cdot i) - (2 i^{4} - 6 i^{3})$

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

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

Multiply $- 1$ by $4$ .

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

Simplify each term.

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

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

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

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

$11 - 4 i - (2 {(- 1)}^{2} - 6 i^{3})$

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

$11 - 4 i - (2 \cdot 1 - 6 i^{3})$

$11 - 4 i - (2 \cdot 1 - 6 i^{3})$

Multiply $2$ by $1$ .

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

Factor out $i^{2}$ .

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

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

$11 - 4 i - (2 - 6 (- 1 \cdot i))$

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

$11 - 4 i - (2 - 6 (- i))$

Multiply $- 1$ by $- 6$ .

$11 - 4 i - (2 + 6 i)$

$11 - 4 i - (2 + 6 i)$

Apply the distributive property.

$11 - 4 i - 1 \cdot 2 - (6 i)$

Multiply $- 1$ by $2$ .

$11 - 4 i - 2 - (6 i)$

Multiply $6$ by $- 1$ .

$11 - 4 i - 2 - 6 i$

$11 - 4 i - 2 - 6 i$

Simplify by adding terms.

Subtract $2$ from $11$ .

$9 - 4 i - 6 i$

Subtract $6 i$ from $- 4 i$ .

$9 - 10 i$

$9 - 10 i$

Related Questions