Question

What is the absolute value of the complex number -4-sqrt-1

a) 14
b) 0
c) 3/2
d) 18

Answer 1

The absolute value of the complex number -4-√i is √17, calculated by taking the square root of the sum of the squares of its real and imaginary parts. None of the given answer choices (14, 0, 3/2, 18) match this calculation, suggesting there may be an error in the options provided.

Step-by-step explanation:

The absolute value of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. The imaginary unit, represented by √i, is equivalent to the square root of -1. Thus, √-1 is simply 'i' in the context of the complex number -4 - √i.

The absolute value is calculated as follows:

1. Identify the real part and the imaginary part of the complex number. For -4 - √i, the real part is -4, and the imaginary part is -1 (since √i corresponds to √-1).
2. The absolute value is √((-4)2 + (-1)2) = √(16 + 1) = √17.

However, looking at the answer choices provided, none matches √17. It seems there might be an error in the available options or in the interpretation of the question.