Why is the square root of -4 an imaginary number instead of -2?

Question

Why is the square root of -4 an imaginary number instead of -2?

In: Mathematics

Answer 1

(-2)^2 = (-2)*(-2) = 4

​

So -2 cant be the square root of -4. Because -2 times -2 is 4.

Essentially, with imaginary numbers, mathematicians “created” a solution to the sqrt of negative numbers. By defining a number i, which has the property that i*i = -1, you can now solve any square roots, in terms of that number i.

That alone doesnt sound very exciting, but it turns out that i has the nice property of going in circles if multiplied with itself (e.g. i = i, i*i = 1, i*i*i = 1*i = 1), and that we can express trigonometric functions with it, which makes them very useful in describing things which rotate and/or repeat itself, such as waves, alternating currents, etc.