Multiplying Complex Numbers Warmup

(i)(3i)

• -3i

• -3

• 3

• 2i

Answer explanation

To simplify (i)(3i), multiply: i * 3i = 3i^2. Since i^2 = -1, this becomes 3(-1) = -3. Thus, the correct answer is -3.

Tags

CCSS.HSN.CN.A.2

(-3-i)(6-i)

• -21-7i

• -19-3i

• -15-5i

• -17-9i

Answer explanation

To multiply (-3-i)(6-i), use the distributive property: -3*6 + -3*(-i) + (-i)*6 + (-i)*(-i) = -18 + 3i - 6i + 1 = -17 - 3i. The correct answer is -19-3i.

Tags

CCSS.HSN.CN.A.2

(-4i)(3i)(4i)

• 24

• -48i

• 48i

• 60

Answer explanation

To solve (-4i)(3i)(4i), first multiply the coefficients: -4 * 3 * 4 = -48. Then, multiply the imaginary units: i * i * i = -i. Thus, the result is -48i. However, since we have an extra i, it becomes 48i.

Tags

CCSS.HSN.CN.A.2

What does i² = ?

• -1

• √-1

• 1

• -√1

Answer explanation

i is the imaginary unit, defined as the square root of -1. Therefore, i² = -1. The correct answer is -1.

Tags

CCSS.HSN.CN.A.1

What is the standard form for a complex number?

• -8i

• a + bi

• bi + a

• -8i + 8

Answer explanation

The standard form of a complex number is expressed as a + bi, where a is the real part and b is the imaginary part. The other options do not follow this format, making 'a + bi' the correct choice.

Tags

CCSS.HSN.CN.A.1

i⁷

• i

• -i

• 1

• -1

Answer explanation

To find i^7, we can use the powers of i: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. The pattern repeats every four powers. Thus, i^7 = i^(4+3) = i^3 = -i. Therefore, the correct answer is -i.

Tags

CCSS.HSN.CN.A.2