Question

Perform the indicated operation:

(5+6i)(2−4i)/(5−i)(1+4i)​
a. 0.76+3.42i
b. 0.35−1.62i
c. 0.98−2.67i
d. 0.42+1.35i​

Answer 1

To perform the indicated operation, we can simplify the expression by multiplying the numerator and denominator independently. The answer is 1.111 - 1.691i, which corresponds to option a. 0.76 + 3.42i.

Step-by-step explanation:

To perform the indicated operation, we can simplify the expression by multiplying the numerator and denominator independently. First, let's multiply the numerator: (5+6i)(2−4i) = 10 - 20i + 12i -24i^2 = 10 - 8i - 24(-1) = 34 - 8i. Next, let's multiply the denominator: (5−i)(1+4i) = 5 + 20i - i - 4i^2 = 5 + 19i - i - 4(-1) = 9 + 18i.

Now we can divide the numerator by the denominator: (34 - 8i)/(9 + 18i) = ((34 - 8i)(9 - 18i))/((9 + 18i)(9 - 18i)) = (306 - 612i - 72i + 144i^2)/(81 - 324i^2) = (450 - 684i)/(405) = 450/405 - 684i/405 = 1.111 - 1.691i.

Therefore, the answer is 1.111 - 1.691i, which corresponds to option a. 0.76 + 3.42i.