Answer :
Final answer:
The product of the complex number (8 – 5i) squared is found using the FOIL method. After simplification and combining like terms, the resulting product is 39 - 80. So, the correct option is option c.
Explanation:
The question asks for the product of the complex number (8 – 5i) squared. To find the product, you follow the standard algebraic rules for multiplying complex numbers. First, we express the square of the complex number as a binomial product: (8 - 5i)² = (8 - 5i)(8 - 5i). Next, we apply the distributive property (also known as the FOIL method) for binomials: (8 - 5i)(8 - 5i) = 8²8 + 8²(-5i) + (-5i)²8 + (-5i)²(-5i)
Simplify the expression: 64 - 40i - 40i + 25i². Since i² = -1 (by definition of the imaginary unit), we can substitute to further simplify: 64 - 40i - 40i - 25. Combine like terms: 64 - 25 - 80i, 39 - 80i. This gives us the product of (8 – 5i) squared, which is 39 - 80i, matching answer choice (c).
