Question

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)

Answer 1

a) 7 + 5i

b) 1 + 24i

a) 34 + i

b) -156 + 12i

Explanation:

a) (5 + 8i) + (2 - 3i)

Add real parts ⇒ 5 + 2 = 7

Add imaginary parts ⇒ 8i + -3i = 5i

∴ (5 + 8i) + (2 - 3I) = 7 + 5i

b) (-3 + 12i) + (4 + 12i)

Add real parts ⇒ -3 + 4 = 1

Add imaginary parts ⇒ 12i + 12i = 24i

∴ (-3 + 12i) + (4 + 12I) = 1 + 24i

Products:

a) (5 + 8i)(2 - 3i)

= 10 - 15i + 16i - 24i² ⇒ (i² = -1)

= 10 + i - 24(-1) = 10 + i + 24

= 34 + i

b) (-3 + 12i)(4 + 12i)

= -12 - 36i + 48i + 144i² ⇒ (i² = -1)

= -12 + 12i + 144(-1) = -12 + 12i - 144

= -156 + 12i