What is the value of the expression given below?

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

Solution:

The given complex expression is,

→ (5+3 i) - (5+3 i) (5-5 i)

Keep in mind, i=√-1, i² = - 1

= (5 + 3 i) [1 - (5-5 i) ]

= (5 + 3 i) [1-5 + 5 i]

= (5 + 3 i) [-4 + 5 i]

=5 * (-4 + 5 i) + 3 i * (-4 + 5 i) →→Used the identity, (a+b) * (c+d) = a * (c+d) + b * (c+d), Also Used distributive property of multiplication over addition and subtraction.

= - 20 + 25 i-12 i + 15 i²

= - 20 + 13 i-15

= - 35 + 13 i

I think the answer would be

= - 35 + 13 i