Algebra Examples

${(6 + 7 i)}^{2}$

Step 1

Rewrite ${(6 + 7 i)}^{2}$ as $(6 + 7 i) (6 + 7 i)$ .

$(6 + 7 i) (6 + 7 i)$

Step 2

Expand $(6 + 7 i) (6 + 7 i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 (6 + 7 i) + 7 i (6 + 7 i)$

Step 2.2

Apply the distributive property.

$6 \cdot 6 + 6 (7 i) + 7 i (6 + 7 i)$

Step 2.3

Apply the distributive property.

$6 \cdot 6 + 6 (7 i) + 7 i \cdot 6 + 7 i (7 i)$

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 $6$ by $6$ .

$36 + 6 (7 i) + 7 i \cdot 6 + 7 i (7 i)$

Step 3.1.2

Multiply $7$ by $6$ .

$36 + 42 i + 7 i \cdot 6 + 7 i (7 i)$

Step 3.1.3

Multiply $6$ by $7$ .

$36 + 42 i + 42 i + 7 i (7 i)$

Step 3.1.4

Multiply $7 i (7 i)$ .

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Step 3.1.4.1

Multiply $7$ by $7$ .

$36 + 42 i + 42 i + 49 i i$

Step 3.1.4.2

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

$36 + 42 i + 42 i + 49 (i^{1} i)$

Step 3.1.4.3

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

$36 + 42 i + 42 i + 49 (i^{1} i^{1})$

Step 3.1.4.4

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

$36 + 42 i + 42 i + 49 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$36 + 42 i + 42 i + 49 i^{2}$

Step 3.1.5

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

$36 + 42 i + 42 i + 49 \cdot - 1$

Step 3.1.6

Multiply $49$ by $- 1$ .

$36 + 42 i + 42 i - 49$

Step 3.2

Subtract $49$ from $36$ .

$- 13 + 42 i + 42 i$

Step 3.3

Add $42 i$ and $42 i$ .

$- 13 + 84 i$