Simplify (3+7i)(-2-2i)-4i(5-9i)

$(3 + 7 i) (- 2 - 2 i) - 4 i (5 - 9 i)$

Step 1

Simplify each term.

Expand $(3 + 7 i) (- 2 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$3 (- 2 - 2 i) + 7 i (- 2 - 2 i) - 4 i (5 - 9 i)$

Apply the distributive property.

$3 \cdot - 2 + 3 (- 2 i) + 7 i (- 2 - 2 i) - 4 i (5 - 9 i)$

Apply the distributive property.

$3 \cdot - 2 + 3 (- 2 i) + 7 i \cdot - 2 + 7 i (- 2 i) - 4 i (5 - 9 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 2$ .

$- 6 + 3 (- 2 i) + 7 i \cdot - 2 + 7 i (- 2 i) - 4 i (5 - 9 i)$

Multiply $- 2$ by $3$ .

$- 6 - 6 i + 7 i \cdot - 2 + 7 i (- 2 i) - 4 i (5 - 9 i)$

Multiply $- 2$ by $7$ .

$- 6 - 6 i - 14 i + 7 i (- 2 i) - 4 i (5 - 9 i)$

Multiply $7 i (- 2 i)$ .

Multiply $- 2$ by $7$ .

$- 6 - 6 i - 14 i - 14 i i - 4 i (5 - 9 i)$

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

$- 6 - 6 i - 14 i - 14 (i^{1} i) - 4 i (5 - 9 i)$

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

$- 6 - 6 i - 14 i - 14 (i^{1} i^{1}) - 4 i (5 - 9 i)$

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

$- 6 - 6 i - 14 i - 14 i^{1 + 1} - 4 i (5 - 9 i)$

Add $1$ and $1$ .

$- 6 - 6 i - 14 i - 14 i^{2} - 4 i (5 - 9 i)$

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

$- 6 - 6 i - 14 i - 14 \cdot - 1 - 4 i (5 - 9 i)$

Multiply $- 14$ by $- 1$ .

$- 6 - 6 i - 14 i + 14 - 4 i (5 - 9 i)$

Add $- 6$ and $14$ .

$8 - 6 i - 14 i - 4 i (5 - 9 i)$

Subtract $14 i$ from $- 6 i$ .

$8 - 20 i - 4 i (5 - 9 i)$

Apply the distributive property.

$8 - 20 i - 4 i \cdot 5 - 4 i (- 9 i)$

Multiply $5$ by $- 4$ .

$8 - 20 i - 20 i - 4 i (- 9 i)$

Multiply $- 4 i (- 9 i)$ .

Multiply $- 9$ by $- 4$ .

$8 - 20 i - 20 i + 36 i i$

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

$8 - 20 i - 20 i + 36 (i^{1} i)$

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

$8 - 20 i - 20 i + 36 (i^{1} i^{1})$

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

$8 - 20 i - 20 i + 36 i^{1 + 1}$

Add $1$ and $1$ .

$8 - 20 i - 20 i + 36 i^{2}$

Simplify each term.

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

$8 - 20 i - 20 i + 36 \cdot - 1$

Multiply $36$ by $- 1$ .

$8 - 20 i - 20 i - 36$

Step 2

Simplify by adding terms.

Subtract $36$ from $8$ .

$- 28 - 20 i - 20 i$

Subtract $20 i$ from $- 20 i$ .

$- 28 - 40 i$

Simplify (3+7i)(-2-2i)-4i(5-9i)

Related Questions

Support LCMGCF.com by disabling your adblocker.