A Non-Real Number is a number comprising a Real and Imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i ^ 2 = ?1.A Non-real number numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication. Non-Real Numbers are also Know as Complex Numbers.
The hardest thing about working with complex numbers is, understanding why you might want to. Let's look at simpler examples of the need to deal with new numbers. If you are like most people, initially number meant Whole Number, 0,1,2,3,... Whole numbers make sense. They provide a way to answer questions of the form "How many ... ? You also learned about the operations of addition and subtraction, and you found that while subtraction is a perfectly good operation, some subtraction problems, like 3 - 5, don't have answers if we only work with whole numbers. Then you find that if you are willing to work with integers, ...,-2, -1, 0, 1, 2, ..., then all subtraction problems do have answers! Furthermore, by considering examples such as temperature scales, you see that negative numbers often make sense.
Now we have fixed subtraction we will deal with division. Some, in fact most, division problems do not have answers that are integers. For example, 3 ÷ 2 is not an integer. We need new numbers! Now we have Rational Numbers also Known as Fractions.
There is more to this story. There are problems with square roots and other operations, but we will not get into that here. The point is that you have had to expand your idea of number on several occasions, and now we are going to do that again.
The problem that leads to complex numbers concerns solutions of equations. Like x^2 +1 =0 where complex numbers are used .
The hardest thing about working with complex numbers is, understanding why you might want to. Let's look at simpler examples of the need to deal with new numbers. If you are like most people, initially number meant Whole Number, 0,1,2,3,... Whole numbers make sense. They provide a way to answer questions of the form "How many ... ? You also learned about the operations of addition and subtraction, and you found that while subtraction is a perfectly good operation, some subtraction problems, like 3 - 5, don't have answers if we only work with whole numbers. Then you find that if you are willing to work with integers, ...,-2, -1, 0, 1, 2, ..., then all subtraction problems do have answers! Furthermore, by considering examples such as temperature scales, you see that negative numbers often make sense.
Now we have fixed subtraction we will deal with division. Some, in fact most, division problems do not have answers that are integers. For example, 3 ÷ 2 is not an integer. We need new numbers! Now we have Rational Numbers also Known as Fractions.
There is more to this story. There are problems with square roots and other operations, but we will not get into that here. The point is that you have had to expand your idea of number on several occasions, and now we are going to do that again.
The problem that leads to complex numbers concerns solutions of equations. Like x^2 +1 =0 where complex numbers are used .
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