Question

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

a. 39
b. 89
c. 39-80i
d. 89-80i

Answer 1

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.

Step-by-step 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