Question

Show all work to multiply quantity 3 plus the square root of negative 16 end quantity times quantity 6 minus the square root of negative 64 end quantity

Answer 1

To multiply (3 + √-16) by (6 - √-64), convert the square roots of negative numbers to imaginary numbers, apply the FOIL method to multiply, and combine like terms. The imaginary units cancel out, leaving a final answer of 50.

Step-by-step explanation:

To multiply (3 + √-16) by (6 - √-64), we first need to simplify the square roots of negative numbers which involve imaginary numbers.

Let's start by simplifying the square roots:

• √-16 = √16 × √-1 = 4i, since √-1 is defined as the imaginary unit, i.
• √-64 = √64 × √-1 = 8i for the same reason as above.

Now, substitute these values back into the original expression and multiply:

1. (3 + 4i) × (6 - 8i)
2. Use the FOIL method (First, Outside, Inside, Last) to expand the product:
3. First: 3 × 6 = 18
4. Outside: 3 × (-8i) = -24i
5. Inside: 4i × 6 = 24i
6. Last: 4i × (-8i) = -32i²

Note that i² = -1, so -32i² becomes +32.

Combine like terms:

• (18) + (-24i) + (24i) + (32)
• The imaginary parts cancel each other out: -24i + 24i = 0
• Final Answer: 18 + 32 = 50

Answer 2

18-32i^2

Step-by-step explanation:

3 + the negative square root of 16 would simplify to 4i

so it will be (3+4i)

6 - the negative square root of 64 would simplify into 8i

so it will be (6-8i)

To solve (3+4i)(6-8i) use FOIL and add like terms