Simplify (5+4i^2)+(9-4i^4)

$(5 + 4 i^{2}) + (9 - 4 i^{4})$

Step 1

Remove parentheses.

$5 + 4 i^{2} + 9 - 4 i^{4}$

Step 2

Simplify each term.

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

$5 + 4 \cdot - 1 + 9 - 4 i^{4}$

Multiply $4$ by $- 1$ .

$5 - 4 + 9 - 4 i^{4}$

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

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

$5 - 4 + 9 - 4 {(i^{2})}^{2}$

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

$5 - 4 + 9 - 4 {(- 1)}^{2}$

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

$5 - 4 + 9 - 4 \cdot 1$

$5 - 4 + 9 - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$5 - 4 + 9 - 4$

$5 - 4 + 9 - 4$

Step 3

Simplify by adding and subtracting.

Subtract $4$ from $5$ .

$1 + 9 - 4$

Add $1$ and $9$ .

$10 - 4$

Subtract $4$ from $10$ .

$6$

$6$

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