Finite Math Examples

$(1 + j) (- \sqrt{3} + j)$

Step 1

Expand $(1 + j) (- \sqrt{3} + j)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$1 (- \sqrt{3} + j) + j (- \sqrt{3} + j)$

Step 1.2

Apply the distributive property.

$1 (- \sqrt{3}) + 1 j + j (- \sqrt{3} + j)$

Step 1.3

Apply the distributive property.

$1 (- \sqrt{3}) + 1 j + j (- \sqrt{3}) + j \cdot j$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- \sqrt{3}$ by $1$ .

$- \sqrt{3} + 1 j + j (- \sqrt{3}) + j \cdot j$

Step 2.1.2

Multiply $j$ by $1$ .

$- \sqrt{3} + j + j (- \sqrt{3}) + j \cdot j$

Step 2.1.3

Multiply $j$ by $j$ .

$- \sqrt{3} + j + j (- \sqrt{3}) + j^{2}$

Step 2.2

Reorder factors in $- \sqrt{3} + j + j (- \sqrt{3}) + j^{2}$ .

$- \sqrt{3} + j - j \sqrt{3} + j^{2}$