Algebra Examples

$(2 + 4 i) + i (2 + i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 + 4 i + i \cdot 2 + i i$

Step 1.2

Move $2$ to the left of $i$ .

$2 + 4 i + 2 \cdot i + i i$

Step 1.3

Multiply $i i$ .

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Step 1.3.1

Raise $i$ to the power of $1$ .

$2 + 4 i + 2 \cdot i + i^{1} i$

Step 1.3.2

Raise $i$ to the power of $1$ .

$2 + 4 i + 2 \cdot i + i^{1} i^{1}$

Step 1.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 + 4 i + 2 \cdot i + i^{1 + 1}$

Step 1.3.4

Add $1$ and $1$ .

$2 + 4 i + 2 \cdot i + i^{2}$

Step 1.4

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

$2 + 4 i + 2 i - 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1$ from $2$ .

$1 + 4 i + 2 i$

Step 2.2

Add $4 i$ and $2 i$ .

$1 + 6 i$