Basic Math Examples

${(3 + 10 i)}^{2}$

Step 1

Rewrite ${(3 + 10 i)}^{2}$ as $(3 + 10 i) (3 + 10 i)$ .

$(3 + 10 i) (3 + 10 i)$

Step 2

Expand $(3 + 10 i) (3 + 10 i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 (3 + 10 i) + 10 i (3 + 10 i)$

Step 2.2

Apply the distributive property.

$3 \cdot 3 + 3 (10 i) + 10 i (3 + 10 i)$

Step 2.3

Apply the distributive property.

$3 \cdot 3 + 3 (10 i) + 10 i \cdot 3 + 10 i (10 i)$

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 $3$ by $3$ .

$9 + 3 (10 i) + 10 i \cdot 3 + 10 i (10 i)$

Step 3.1.2

Multiply $10$ by $3$ .

$9 + 30 i + 10 i \cdot 3 + 10 i (10 i)$

Step 3.1.3

Multiply $3$ by $10$ .

$9 + 30 i + 30 i + 10 i (10 i)$

Step 3.1.4

Multiply $10 i (10 i)$ .

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Step 3.1.4.1

Multiply $10$ by $10$ .

$9 + 30 i + 30 i + 100 i i$

Step 3.1.4.2

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

$9 + 30 i + 30 i + 100 (i^{1} i)$

Step 3.1.4.3

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

$9 + 30 i + 30 i + 100 (i^{1} i^{1})$

Step 3.1.4.4

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

$9 + 30 i + 30 i + 100 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$9 + 30 i + 30 i + 100 i^{2}$

Step 3.1.5

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

$9 + 30 i + 30 i + 100 \cdot - 1$

Step 3.1.6

Multiply $100$ by $- 1$ .

$9 + 30 i + 30 i - 100$

Step 3.2

Subtract $100$ from $9$ .

$- 91 + 30 i + 30 i$

Step 3.3

Add $30 i$ and $30 i$ .

$- 91 + 60 i$