MATH SOLVE

4 months ago

Q:
# Compute each of the following sums and differences:a. (5+8i) + (2-3i) b. (-3+12i) + (4+12i)Compute each of the following products:a. (5+8i)(2-3i) b. (-3+12i)(4+12i)

Accepted Solution

A:

Answer:a) 7 + 5ib) 1 + 24ia) 34 + ib) -156 + 12iStep-by-step explanation:a) (5 + 8i) + (2 - 3i) Add real parts ⇒ 5 + 2 = 7Add imaginary parts ⇒ 8i + -3i = 5i∴ (5 + 8i) + (2 - 3I) = 7 + 5ib) (-3 + 12i) + (4 + 12i)Add real parts ⇒ -3 + 4 = 1Add imaginary parts ⇒ 12i + 12i = 24i∴ (-3 + 12i) + (4 + 12I) = 1 + 24iProducts:a) (5 + 8i)(2 - 3i) = 10 - 15i + 16i - 24i² ⇒ (i² = -1) = 10 + i - 24(-1) = 10 + i + 24 = 34 + ib) (-3 + 12i)(4 + 12i) = -12 - 36i + 48i + 144i² ⇒ (i² = -1) = -12 + 12i + 144(-1) = -12 + 12i - 144 = -156 + 12i