Basic Math Examples

(3 - 2 i) \cdot (4 - 2 i)

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

Step 1

Expand

$(3 - 2 i) (4 - 2 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (4 - 2 i) - 2 i (4 - 2 i)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

$3$ by

$4$ .

$12 + 3 (- 2 i) - 2 i \cdot 4 - 2 i (- 2 i)$

Step 2.1.2

Multiply

$- 2$ by

$3$ .

$12 - 6 i - 2 i \cdot 4 - 2 i (- 2 i)$

Step 2.1.3

Multiply

$4$ by

$- 2$ .

$12 - 6 i - 8 i - 2 i (- 2 i)$

Step 2.1.4

Multiply

$- 2 i (- 2 i)$ .

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Step 2.1.4.1

Multiply

$- 2$ by

$- 2$ .

$12 - 6 i - 8 i + 4 i i$

Step 2.1.4.2

Raise

$i$ to the power of

$1$ .

$12 - 6 i - 8 i + 4 (i^{1} i)$

Step 2.1.4.3

Raise

$i$ to the power of

$1$ .

$12 - 6 i - 8 i + 4 (i^{1} i^{1})$

Step 2.1.4.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 - 6 i - 8 i + 4 i^{1 + 1}$

Step 2.1.4.5

Add

$1$ and

$1$ .

$12 - 6 i - 8 i + 4 i^{2}$

$12 - 6 i - 8 i + 4 i^{2}$

Step 2.1.5

Rewrite

$i^{2}$ as

$- 1$ .

$12 - 6 i - 8 i + 4 \cdot - 1$

Step 2.1.6

Multiply

$4$ by

$- 1$ .

$12 - 6 i - 8 i - 4$

$12 - 6 i - 8 i - 4$

Step 2.2

Subtract

$4$ from

$12$ .

$8 - 6 i - 8 i$

Step 2.3

Subtract

$8 i$ from

$- 6 i$ .

$8 - 14 i$

$8 - 14 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$