Question

18. What is the product of (6 + 5i) and (3 - 7i) ?

A: 53+27i
B: - 17 - 27i
C: -17+27i
D: 53 - 27i

19. Which is equivalent to (1 - 14i)(5 - 3i) ?

A: 50 – 70i +42i2
B: -37 - 73i
C: 47+ 3i
D: 5+42i2

Answer 1

To find the product of complex numbers, use the distributive property and simplify. The product of (6 + 5i) and (3 - 7i) is 53 + 27i. The product of (1 - 14i) and (5 - 3i) is -37 - 73i.

Step-by-step explanation:

To find the product of two complex numbers, we use the distributive property and simplify by combining like terms. For the first question, (6 + 5i)(3 - 7i) = 18 - 42i + 15i - 35i^2. Since i^2 = -1, we can simplify further to get 18 - 27i - 35(-1) = 53 + 27i. Therefore, the answer is Option A: 53+27i.

For the second question, (1 - 14i)(5 - 3i) = 5 - 3i - 70i + 42i^2. Using i^2 = -1, we simplify to get 5 - 73i + 42(-1) = -37 - 73i. Therefore, the answer is Option B: -37 - 73i.

Answer 2

18. Is D 19. Is B
Hope this helps

Explanation
So for 18 you use FOIL
(6+5i)(3-7i)
18-42i+15i-35i^2 i^2=-1
18-27i-(35)(-1)
substitute -1 in and add like terms
53-27i

Then for 19
(1-14i)(5-3i)
5-3i-70i+42i^2
5-73i+(42)(-1)
-37-73i