Question
Mathematics
Which set of numbers are imaginary numbers?
$\left\{-2,-3,-4\right\}${-2,-3,-4}
$\left\{\sqrt{2},\pi ,\sqrt{3}\right\}${sqrt2,pi,sqrt3}
$\left\{0,1,2,3\right\}${0,1,2,3}
$\left\{\frac{1}{2},\frac{1}{4},\frac{1}{8}\right\}${(1)/(2),(1)/(4),(1)/(8)}
$\left\{\sqrt{-1},\sqrt{-4},\sqrt{-5}\right\}${sqrt(-1),sqrt(-4),sqrt(-5)}
Solve problem with AI
The set of numbers that are imaginary numbers is $\left\{\sqrt{-1},\sqrt{-4},\sqrt{-5}\right\}${sqrt(-1),sqrt(-4),sqrt(-5)}.
Answer: $\left\{\sqrt{-1},\sqrt{-4},\sqrt{-5}\right\}${sqrt(-1),sqrt(-4),sqrt(-5)}
• Imaginary numbers are the numbers that can be written in the form $bi$bi, where $b$b is a real number and $i$i is the imaginary unit, defined as $i=\sqrt{-1}$i=sqrt(-1).
• The set $\left\{-2,-3,-4\right\}${-2,-3,-4} is not a set of imaginary numbers, as these numbers are real numbers.
• The set $\left\{\sqrt{2},\pi ,\sqrt{3}\right\}${sqrt2,pi,sqrt3} is not a set of imaginary numbers, as these numbers are real numbers.
• The set $\left\{0,1,2,3\right\}${0,1,2,3} is not a set of imaginary numbers, as these numbers are real numbers.
• The set $\left\{\frac{1}{2},\frac{1}{4},\frac{1}{8}\right\}${(1)/(2),(1)/(4),(1)/(8)} is not a set of imaginary numbers, as these numbers are real numbers.
• The set $\left\{\sqrt{-1},\sqrt{-4},\sqrt{-5}\right\}${sqrt(-1),sqrt(-4),sqrt(-5)} is a set of imaginary numbers, as these numbers can be written as $bi$bi where $b$b is a real number. Specifically, $\sqrt{-1}=i$sqrt(-1)=i, $\sqrt{-4}=2i$sqrt(-4)=2i, and $\sqrt{-5}=\sqrt{5}i$sqrt(-5)=sqrt5i.