Multiply and simplify the product.
(8 – 5i)2
select the product.

a. 39

b. 89

c. 39-80i

d. 89-80i

Simplifying the square of a complex binomial is done similarly to a purely real binomial, except that one was to remember the relation i² = -1.

Solving the equation (8 – 5i)² is done below:

Rewriting (8 – 5i)²:

(8 - 5i)(8 - 5i) = 64 - 40i - 40i + 25i²

Simplifying and applying i² = -1:
64 - 80i + 25(-1)
64 - 80i - 25
39 - 80i

From the choices, the answer is C. 

The correct answer is d. (0,5)