Question

Write a complex number with an absolute value between 3 and 8.

A. 3 − 4i
B. 12 − i
C. 8 + i
D. 1 + i

Answer 1

The complex number with an absolute value between 3 and 8 is 3 - 4i.

Step-by-step explanation:

To find a complex number with an absolute value between 3 and 8, we need to find a number that lies on the complex plane within a circle of radius between 3 and 8. Let's examine the options:

1. Absolute value of 3 - 4i is √(3^2 + (-4)^2) = 5. This falls within the desired range.
2. Absolute value of 12 - i is √(12^2 + (-1)^2) = √146 which is greater than 8, so this is not the answer.
3. Absolute value of 8 + i is √(8^2 + 1^2) = √65 which is greater than 8, so this is not the answer.
4. Absolute value of 1 + i is √(1^2 + 1^2) = √2 which is less than 3, so this is not the answer.

Therefore, the complex number with an absolute value between 3 and 8 is 3 - 4i. Option A is the correct answer.

Answer 2

A cuz it had to be idk