Use the Distributive Property to simplify (6−3i)(3−5i) .(1 point)

Question

Responses

3−39i
3 minus 39 i

33−39i
33 minus 39 i

9−8i
9 minus 8 i

18+15i2

Answer 1

To simplify \((6 - 3i)(3 - 5i)\) using the Distributive Property, we'll distribute each term in the first parenthesis to each term in the second parenthesis.

1. Multiply \(6\) by \(3\): \[ 6 \times 3 = 18 \]

2. Multiply \(6\) by \(-5i\): \[ 6 \times -5i = -30i \]

3. Multiply \(-3i\) by \(3\): \[ -3i \times 3 = -9i \]

4. Multiply \(-3i\) by \(-5i\): \[ -3i \times -5i = 15i^2 \] Since \(i^2 = -1\), we have: \[ 15i^2 = 15(-1) = -15 \]

Now, combine all these results: \[ 18 - 30i - 9i - 15 \]

Combine like terms:

• The real parts: \(18 - 15 = 3\)
• The imaginary parts: \(-30i - 9i = -39i\)

Putting it all together, we have: \[ 3 - 39i \]

Thus, the simplified expression is: \[ \boxed{3 - 39i} \]