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.