There are lots of different meanings for each kind of number, to sort this out, I'm going to list all the different kinds of numbers and their definitions here as a reference.
Includes all rational and irrational numbers. May be positive, negative or zero.
Any number that can be named, for instance five, six or three-hundred sixty-two, five point four or one-fourths. It can be any whole number, fraction or decimal with it's negative pair. 1, -1, 1.1 and are all rational numbers.
Integers are numbers without decimal or fractional parts. An example set of some integers: 0, 1, -1, 2, 54, 99, 1000, -1000, 13, 453, -234. All integers would exist along an infinitely long number line with 0 at the center going from the negative integers to the positive integers.
Any positive integer. Sometimes when the 0 is included in this set, the numbers are referred to as whole numbers or counting numbers.
A number that cannot be expressed as a fraction where m and n are integers and n is non-zero. These numbers cannot be represented as simple or infinitely repeating decimals. These numbers are all the Real numbers that are not considered rational.
A number taking the form bi where b is a real number, and i is the square root of minus one. The imaginary numbers repeat in a constant pattern as shown here:
Calculating the imaginary number for x number of powers for i is a matter of knowing a few things, first the imaginary unit which is . This is why . Now if you multiply 2 numbers squared together, you pull the number inside the square root out, which gives you this:
Knowing how two squared numbers interact with each other helps us solve the 3rd power like so:
Solving for now is a breeze:
These numbers are made up of real and imaginary numbers and can take the form of where a and b are real numbers, and i is imaginary.