Answer :
Final answer:
To multiply and simplify (8 - 5i)², use the formula (a - b)² = a² - 2ab + b² and plug in the values 8 and 5i to get the result 39 - 80i.
Explanation:
To multiply and simplify the product (8 - 5i)², we use the formula (a - b)² = a² - 2ab + b², where a = 8 and b = 5i. Plugging in the values, we get:
(8 - 5i)² = (8)² - 2(8)(-5i) + (-5i)²
Simplifying further:
(8 - 5i)² = 64 - 80i + 25i²
Remembering that i² = -1, we can replace i² with -1:
(8 - 5i)² = 64 - 80i + 25(-1)
Finally, simplifying the expression, we get:
(8 - 5i)² = 64 - 80i - 25
(8 - 5i)² = 39 - 80i
