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An imaginary number is simply a number that contains 'i' which is simply shorthand for the square root of minus one. In the same way, we can write the square root of other negative numbers using i as a factor. For example;
Sqrt(-64) = Sqrt(-1*64) = Sqrt(-1)*Sqrt(64) = i*8 = 8i
There are also 'complex numbers' which are simply combinations of real numbers (all positive and negative numbers) and imaginary numbers. For example;
2+3i
Is a complex number. Although these numbers seem not to "exist" (it's impossible to have a set of 8i Golf balls, or for you to weigh 3i kg) they are very useful in the fields of mathematics, physics, and engineering, and allowing their existence can save a lot of trouble when it comes to doing difficult math.
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Is every complex number a pure imaginary number?
No. For example the number 1+i. Pure imaginary complex numbers are of the form 0 + a*i, where a is a non-zero real number.
Is pi an Example of a number that is not real?
No. The square root of negative one is an example of an imaginary (not real) number. Pi is irrational, but real.
Can a number be imaginary but not pure imaginary?
Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.
Is a square root of a negative number a real number?
no, it is an imaginary number represented by an i. For example, the square root of -4 is 2i.
What is an unreal in math?
The only thing I can think of that you might mean is an imaginary or complex number. Since there is no solution to √(-1) mathematicians labeled it as i which is the imaginary number, and any number that includes purely i is also imaginary. Complex numbers are a mix of both real and imaginary numbers. for example 3 is real, 5i is imaginary and 3+5i is complex. Hopefully this answers what you meant.
