Algebra Examples

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

Step 1

Rewrite ${(2 + 3 i)}^{2}$ as $(2 + 3 i) (2 + 3 i)$ .

$(2 + 3 i) (2 + 3 i)$

Step 2

Expand $(2 + 3 i) (2 + 3 i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (2 + 3 i) + 3 i (2 + 3 i)$

Step 2.2

Apply the distributive property.

$2 \cdot 2 + 2 (3 i) + 3 i (2 + 3 i)$

Step 2.3

Apply the distributive property.

$2 \cdot 2 + 2 (3 i) + 3 i \cdot 2 + 3 i (3 i)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$4 + 2 (3 i) + 3 i \cdot 2 + 3 i (3 i)$

Step 3.1.2

Multiply $3$ by $2$ .

$4 + 6 i + 3 i \cdot 2 + 3 i (3 i)$

Step 3.1.3

Multiply $2$ by $3$ .

$4 + 6 i + 6 i + 3 i (3 i)$

Step 3.1.4

Multiply $3 i (3 i)$ .

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Step 3.1.4.1

Multiply $3$ by $3$ .

$4 + 6 i + 6 i + 9 i i$

Step 3.1.4.2

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

$4 + 6 i + 6 i + 9 (i^{1} i)$

Step 3.1.4.3

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

$4 + 6 i + 6 i + 9 (i^{1} i^{1})$

Step 3.1.4.4

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

$4 + 6 i + 6 i + 9 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$4 + 6 i + 6 i + 9 i^{2}$

Step 3.1.5

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

$4 + 6 i + 6 i + 9 \cdot - 1$

Step 3.1.6

Multiply $9$ by $- 1$ .

$4 + 6 i + 6 i - 9$

Step 3.2

Subtract $9$ from $4$ .

$- 5 + 6 i + 6 i$

Step 3.3

Add $6 i$ and $6 i$ .

$- 5 + 12 i$