Hello. I'm a calculus 1 student in college, and I recently came across a function where x was raised to the (2/3) power. Does anyone in this forum know why a negative number raised to the 2/3 becomes an imaginary number? Type the problem into any calculator, including Google. You'll get an error or an imaginary number.
But why does this give you an imaginary number? It's the same as ((-1)^2)^(1/3) or ((-1)^(1/3))^(2). It seems like when you square (-1) you get (1), and the cube root of (-1) is just (-1). Can anyone on this forum explain why this happens?
Thank you. This is the answer I got from Google. Can you tell me what math subject I can study to learn about this? I want to build my math skills. I will find books and videos if you tell me the specific subject. For example, in college algebra and trigonometry, we never studied any of this. I have become very interested in math and I want to study math.