Basic Math Examples

$- {(5 + 7 i)}^{2}$

Step 1

Rewrite ${(5 + 7 i)}^{2}$ as $(5 + 7 i) (5 + 7 i)$ .

$- ((5 + 7 i) (5 + 7 i))$

Step 2

Expand $(5 + 7 i) (5 + 7 i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- (5 (5 + 7 i) + 7 i (5 + 7 i))$

Step 2.2

Apply the distributive property.

$- (5 \cdot 5 + 5 (7 i) + 7 i (5 + 7 i))$

Step 2.3

Apply the distributive property.

$- (5 \cdot 5 + 5 (7 i) + 7 i \cdot 5 + 7 i (7 i))$

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 $5$ by $5$ .

$- (25 + 5 (7 i) + 7 i \cdot 5 + 7 i (7 i))$

Step 3.1.2

Multiply $7$ by $5$ .

$- (25 + 35 i + 7 i \cdot 5 + 7 i (7 i))$

Step 3.1.3

Multiply $5$ by $7$ .

$- (25 + 35 i + 35 i + 7 i (7 i))$

Step 3.1.4

Multiply $7 i (7 i)$ .

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Step 3.1.4.1

Multiply $7$ by $7$ .

$- (25 + 35 i + 35 i + 49 i i)$

Step 3.1.4.2

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

$- (25 + 35 i + 35 i + 49 (i^{1} i))$

Step 3.1.4.3

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

$- (25 + 35 i + 35 i + 49 (i^{1} i^{1}))$

Step 3.1.4.4

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

$- (25 + 35 i + 35 i + 49 i^{1 + 1})$

Step 3.1.4.5

Add $1$ and $1$ .

$- (25 + 35 i + 35 i + 49 i^{2})$

Step 3.1.5

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

$- (25 + 35 i + 35 i + 49 \cdot - 1)$

Step 3.1.6

Multiply $49$ by $- 1$ .

$- (25 + 35 i + 35 i - 49)$

Step 3.2

Subtract $49$ from $25$ .

$- (- 24 + 35 i + 35 i)$

Step 3.3

Add $35 i$ and $35 i$ .

$- (- 24 + 70 i)$

Step 4

Apply the distributive property.

$- - 24 - (70 i)$

Step 5

Multiply.

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Step 5.1

Multiply $- 1$ by $- 24$ .

$24 - (70 i)$

Step 5.2

Multiply $70$ by $- 1$ .

$24 - 70 i$