Complex Numbers Question 6

For any real number $x$ such that $x\lt -5$ in the equation below, which of the following statements must be true of the number represented by $y$ ?

y=-\sqrt{x+5}

y

is irrational.

y\gt 0

y=0

y\lt 0

y

is imaginary.

Approach

If $x\lt -5$ , then the expression $\sqrt{x+5}$ will be negative.

This results in an imaginary number $i=\sqrt{-1}$ .