Write in the form a +bi

Question

(5 + 3i ) (7-3i)

A 5 - 3i

B 3i - 5

C -5 - 3i

D 8?  

 

 

Answer 1

The expression is (5 + 3i)(7 - 3i).

(5 + 3i)(7 - 3i) = 5(7 - 3i) + 3i(7 - 3i)

Apply distributive property : a(b - c) = ab - ac.

                         = 5(7) - 5(3i) + 3i(7) - 3i(3i)

                         = 35 - 15i + 21i - 9i²

                         = 35 - 15i + 21i - 9(- 1)                             [ i² = -1 ]

                         = (35 + 9) + ( -15i + 21i)

                         = 44 + 6i.

The complex form of (5 + 3i)(7 - 3i) is 44 + 6i.