I keep googling it and I still don’t understand what they are and their differences 😭😭
In: 18
To understand that you first need to understand what a real number is.
A natural number is all the numbers you can count. (1,2,3…).
A whole number does include the negative numbers and zero.
A rational number is any number that can be written as the ratio of two whole numbers. For example 1/3 or 22/7.
A real number is any number on the number line. Famous examples are pi and e, but also numbers like root(2) are real numbers but not rational numbers.
When taking the root you are asking “What number can I multiply with itself to get the number under the root?”.
If you are multiplying a positive number with itself you will get a positive result. If you multiply a negative number with itself it will also be a positive number (negative*negative=positive).
The answer to root(-1) seems impossible to find. And when you are looking at the real numbers it is. So mathematicians invented complex numbers. They said that root(-1)=i. You are no longer dealing with the number line but with a number plane.
When you take the root of any negative number you can get an answer on the number plane. There is a complex number (also known as an imaginary number, that might be where i is from).
Complex numbers are very useful in things like electronics, but in some fields you don’t want to look for complex answers, so you just say that this root doesn’t have an answer in the real numbers and you leave it at that.
If you ever see a big electric motor and you look at it’s plate you will see cos(phi) on there. That phi is the angle how far the apparent power is off the number line in complex math.
Latest Answers