Write in Standard Form 2i(-7-2i)^2

$2 i {(- 7 - 2 i)}^{2}$

Step 1

Rewrite ${(- 7 - 2 i)}^{2}$ as $(- 7 - 2 i) (- 7 - 2 i)$ .

$2 i ((- 7 - 2 i) (- 7 - 2 i))$

Step 2

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

Apply the distributive property.

$2 i (- 7 (- 7 - 2 i) - 2 i (- 7 - 2 i))$

Apply the distributive property.

$2 i (- 7 \cdot - 7 - 7 (- 2 i) - 2 i (- 7 - 2 i))$

Apply the distributive property.

$2 i (- 7 \cdot - 7 - 7 (- 2 i) - 2 i \cdot - 7 - 2 i (- 2 i))$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $- 7$ .

$2 i (49 - 7 (- 2 i) - 2 i \cdot - 7 - 2 i (- 2 i))$

Multiply $- 2$ by $- 7$ .

$2 i (49 + 14 i - 2 i \cdot - 7 - 2 i (- 2 i))$

Multiply $- 7$ by $- 2$ .

$2 i (49 + 14 i + 14 i - 2 i (- 2 i))$

Multiply $- 2 i (- 2 i)$ .

Multiply $- 2$ by $- 2$ .

$2 i (49 + 14 i + 14 i + 4 i i)$

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

$2 i (49 + 14 i + 14 i + 4 (i^{1} i))$

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

$2 i (49 + 14 i + 14 i + 4 (i^{1} i^{1}))$

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

$2 i (49 + 14 i + 14 i + 4 i^{1 + 1})$

Add $1$ and $1$ .

$2 i (49 + 14 i + 14 i + 4 i^{2})$

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

$2 i (49 + 14 i + 14 i + 4 \cdot - 1)$

Multiply $4$ by $- 1$ .

$2 i (49 + 14 i + 14 i - 4)$

Subtract $4$ from $49$ .

$2 i (45 + 14 i + 14 i)$

Add $14 i$ and $14 i$ .

$2 i (45 + 28 i)$

Step 4

Apply the distributive property.

$2 i \cdot 45 + 2 i (28 i)$

Step 5

Multiply $45$ by $2$ .

$90 i + 2 i (28 i)$

Step 6

Multiply $2 i (28 i)$ .

Multiply $28$ by $2$ .

$90 i + 56 i i$

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

$90 i + 56 (i^{1} i)$

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

$90 i + 56 (i^{1} i^{1})$

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

$90 i + 56 i^{1 + 1}$

Add $1$ and $1$ .

$90 i + 56 i^{2}$

Step 7

Simplify each term.

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

$90 i + 56 \cdot - 1$

Multiply $56$ by $- 1$ .

$90 i - 56$

Step 8

Reorder $90 i$ and $- 56$ .

$- 56 + 90 i$

Write in Standard Form 2i(-7-2i)^2

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