Simplify (2+i)+(i^4+i^3)

$(2 + i) + (i^{4} + i^{3})$

Step 1

Remove parentheses.

$2 + i + i^{4} + i^{3}$

Step 2

Simplify each term.

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

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

$2 + i + {(i^{2})}^{2} + i^{3}$

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

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

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

$2 + i + 1 + i^{3}$

$2 + i + 1 + i^{3}$

Factor out $i^{2}$ .

$2 + i + 1 + i^{2} \cdot i$

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

$2 + i + 1 - 1 \cdot i$

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

$2 + i + 1 - i$

$2 + i + 1 - i$

Step 3

Simplify by adding terms.

Add $2$ and $1$ .

$3 + i - i$

Subtract $i$ from $i$ .

$3 + 0$

Add $3$ and $0$ .

$3$

$3$

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