Simplify (6+2i)(6-2i)-(3-4i)(3+4i)

$(6 + 2 i) (6 - 2 i) - (3 - 4 i) (3 + 4 i)$

Simplify each term.

Expand $(6 + 2 i) (6 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$6 (6 - 2 i) + 2 i (6 - 2 i) - (3 - 4 i) (3 + 4 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 2 i) + 2 i (6 - 2 i) - (3 - 4 i) (3 + 4 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 2 i) + 2 i \cdot 6 + 2 i (- 2 i) - (3 - 4 i) (3 + 4 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 (- 2 i) + 2 i \cdot 6 + 2 i (- 2 i) - (3 - 4 i) (3 + 4 i)$

Multiply $- 2$ by $6$ .

$36 - 12 i + 2 i \cdot 6 + 2 i (- 2 i) - (3 - 4 i) (3 + 4 i)$

Multiply $6$ by $2$ .

$36 - 12 i + 12 i + 2 i (- 2 i) - (3 - 4 i) (3 + 4 i)$

Multiply $2 i (- 2 i)$ .

Multiply $- 2$ by $2$ .

$36 - 12 i + 12 i - 4 i i - (3 - 4 i) (3 + 4 i)$

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

$36 - 12 i + 12 i - 4 (i^{1} i) - (3 - 4 i) (3 + 4 i)$

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

$36 - 12 i + 12 i - 4 (i^{1} i^{1}) - (3 - 4 i) (3 + 4 i)$

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

$36 - 12 i + 12 i - 4 i^{1 + 1} - (3 - 4 i) (3 + 4 i)$

Add $1$ and $1$ .

$36 - 12 i + 12 i - 4 i^{2} - (3 - 4 i) (3 + 4 i)$

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

$36 - 12 i + 12 i - 4 \cdot - 1 - (3 - 4 i) (3 + 4 i)$

Multiply $- 4$ by $- 1$ .

$36 - 12 i + 12 i + 4 - (3 - 4 i) (3 + 4 i)$

Add $36$ and $4$ .

$40 - 12 i + 12 i - (3 - 4 i) (3 + 4 i)$

Add $- 12 i$ and $12 i$ .

$40 + 0 - (3 - 4 i) (3 + 4 i)$

Add $40$ and $0$ .

$40 - (3 - 4 i) (3 + 4 i)$

Apply the distributive property.

$40 + (- 1 \cdot 3 - (- 4 i)) (3 + 4 i)$

Multiply $- 1$ by $3$ .

$40 + (- 3 - (- 4 i)) (3 + 4 i)$

Multiply $- 4$ by $- 1$ .

$40 + (- 3 + 4 i) (3 + 4 i)$

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

Apply the distributive property.

$40 - 3 (3 + 4 i) + 4 i (3 + 4 i)$

Apply the distributive property.

$40 - 3 \cdot 3 - 3 (4 i) + 4 i (3 + 4 i)$

Apply the distributive property.

$40 - 3 \cdot 3 - 3 (4 i) + 4 i \cdot 3 + 4 i (4 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $3$ .

$40 - 9 - 3 (4 i) + 4 i \cdot 3 + 4 i (4 i)$

Multiply $4$ by $- 3$ .

$40 - 9 - 12 i + 4 i \cdot 3 + 4 i (4 i)$

Multiply $3$ by $4$ .

$40 - 9 - 12 i + 12 i + 4 i (4 i)$

Multiply $4 i (4 i)$ .

Multiply $4$ by $4$ .

$40 - 9 - 12 i + 12 i + 16 i i$

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

$40 - 9 - 12 i + 12 i + 16 (i^{1} i)$

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

$40 - 9 - 12 i + 12 i + 16 (i^{1} i^{1})$

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

$40 - 9 - 12 i + 12 i + 16 i^{1 + 1}$

Add $1$ and $1$ .

$40 - 9 - 12 i + 12 i + 16 i^{2}$

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

$40 - 9 - 12 i + 12 i + 16 \cdot - 1$

Multiply $16$ by $- 1$ .

$40 - 9 - 12 i + 12 i - 16$

Subtract $16$ from $- 9$ .

$40 - 25 - 12 i + 12 i$

Add $- 12 i$ and $12 i$ .

$40 - 25 + 0$

Add $- 25$ and $0$ .

$40 - 25$

Subtract $25$ from $40$ .

$15$

Simplify (6+2i)(6-2i)-(3-4i)(3+4i)

Related Questions

Support LCMGCF.com by disabling your adblocker.