Solved on Feb 07, 2024

Multiply $2 i(-6 i+6)$ and write the expression in standard form. Choose the correct answer.

STEP 1

Assumptions
1. We are given the expression $2i(-6i + 6)$ .
2. We need to multiply the terms and write the expression in standard form.
3. The standard form for a complex number is $a + bi$ , where $a$ and $b$ are real numbers, and $i$ is the imaginary unit with the property $i^2 = -1$ .

STEP 2

Distribute the $2i$ across the terms inside the parentheses.
$2i(-6i + 6) = 2i \cdot (-6i) + 2i \cdot 6$

STEP 3

Multiply the coefficients and apply the imaginary unit property $i^2 = -1$ .
$2i \cdot (-6i) = -12i^2$

STEP 4

Multiply the second set of terms.
$2i \cdot 6 = 12i$

STEP 5

Combine the results from STEP_3 and STEP_4.
$-12i^2 + 12i$

STEP 6

Substitute $i^2$ with $-1$ as per the property of the imaginary unit.
$-12(-1) + 12i$

STEP 7

Simplify the expression by multiplying $-12$ by $-1$ .
$12 + 12i$
The expression in standard form is $12 + 12i$ .
The correct answer is D. $12+12i$ .

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Multiply $2 i(-6 i+6)$ and write the expression in standard form. Choose the correct answer.

STEP 1

Assumptions
1. We are given the expression $2i(-6i + 6)$ .
2. We need to multiply the terms and write the expression in standard form.
3. The standard form for a complex number is $a + bi$ , where $a$ and $b$ are real numbers, and $i$ is the imaginary unit with the property $i^2 = -1$ .

STEP 2

Distribute the $2i$ across the terms inside the parentheses.
$2i(-6i + 6) = 2i \cdot (-6i) + 2i \cdot 6$

STEP 3

Multiply the coefficients and apply the imaginary unit property $i^2 = -1$ .
$2i \cdot (-6i) = -12i^2$

STEP 4

Multiply the second set of terms.
$2i \cdot 6 = 12i$

STEP 5

Combine the results from STEP_3 and STEP_4.
$-12i^2 + 12i$

STEP 6

Substitute $i^2$ with $-1$ as per the property of the imaginary unit.
$-12(-1) + 12i$

STEP 7

Simplify the expression by multiplying $-12$ by $-1$ .
$12 + 12i$
The expression in standard form is $12 + 12i$ .
The correct answer is D. $12+12i$ .

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Multiply 2i(−6i+6)2 i(-6 i+6)2i(−6i+6) and write the expression in standard form. Choose the correct answer.

STEP 1

STEP 2

Distribute the 2i2i2i across the terms inside the parentheses.2i(−6i+6)=2i⋅(−6i)+2i⋅62i(-6i + 6) = 2i \cdot (-6i) + 2i \cdot 62i(−6i+6)=2i⋅(−6i)+2i⋅6

STEP 3

Multiply the coefficients and apply the imaginary unit property i2=−1i^2 = -1i2=−1.2i⋅(−6i)=−12i22i \cdot (-6i) = -12i^22i⋅(−6i)=−12i2

STEP 4

Multiply the second set of terms.2i⋅6=12i2i \cdot 6 = 12i2i⋅6=12i

STEP 5

Combine the results from STEP_3 and STEP_4.−12i2+12i-12i^2 + 12i−12i2+12i

STEP 6

Substitute i2i^2i2 with −1-1−1 as per the property of the imaginary unit.−12(−1)+12i-12(-1) + 12i−12(−1)+12i

STEP 7

Simplify the expression by multiplying −12-12−12 by −1-1−1.12+12i12 + 12i12+12iThe expression in standard form is 12+12i12 + 12i12+12i.The correct answer is D. 12+12i12+12i12+12i.

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Multiply $2 i(-6 i+6)$ and write the expression in standard form. Choose the correct answer.

Distribute the $2i$ across the terms inside the parentheses.
$2i(-6i + 6) = 2i \cdot (-6i) + 2i \cdot 6$

Multiply the coefficients and apply the imaginary unit property $i^2 = -1$ .
$2i \cdot (-6i) = -12i^2$

Multiply the second set of terms.
$2i \cdot 6 = 12i$

Combine the results from STEP_3 and STEP_4.
$-12i^2 + 12i$

Substitute $i^2$ with $-1$ as per the property of the imaginary unit.
$-12(-1) + 12i$

Simplify the expression by multiplying $-12$ by $-1$ .
$12 + 12i$
The expression in standard form is $12 + 12i$ .
The correct answer is D. $12+12i$ .