What is an imaginary number?
Q: What is an imaginary number?
A: An imaginary number is a combination of a real number and the imaginary unit, called i, where i is defined as i^2=-1.
Q: How are imaginary numbers different from negative real numbers?
A: Imaginary numbers are defined separately from negative real numbers in that they are a square root of a negative real number (instead of a positive real number). This is not possible with real numbers, as there is no real number that will multiply by itself to get a negative number.
Q: What does it mean when we say "go east by -i mile"?
A: When we say "go east by -i mile", it means the same thing as if we had said "go south by 1 mile".
Q: How do you add two imaginary numbers?
A: To add two imaginary numbers, you can say "go east by one mile and north by one mile". Multiplying two imaginary numbers is similar to multiplying a positive number with a negative number.
Q: What are complex numbers?
A: Complex numbers are mixed numbers made up of both real and imaginary components such as 2+3i. They are created when you add together a real and an imaginary component.
Q: In what fields do mathematicians use the concept of an imaginary unit?
A: Mathematicians use the concept of an imaginary unit in many branches of science and engineering such as electrical engineering, quantum physics, high energy physics, etc. It is also used in equations which cannot be solved without it.
