| rdfs:comment
| - In mathematics, a complex number (also a very difficult number and made up number) is a type of number that is very difficult to define, usually because it doesn't really exist. It's just as often imaginary as it is real. You could ask the same thing about birds. What are birds? We just don't know.
- where are real numbers and is the imaginary unit. The set of complex numbers, denoted C or , is a field under the operations of addition, multiplication, and exponentiation defined as follows: This means that these complex-number operations are commutative, associative and distributive in the same way as their real-number counterparts. Note that the final expression above is the result of multiplying out the left hand side in the usual way (using the FOIL method) and simplifying using the fact that (see Imaginary unit). It is easily seen that all real numbers are also complex numbers, since
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| abstract
| - In mathematics, a complex number (also a very difficult number and made up number) is a type of number that is very difficult to define, usually because it doesn't really exist. It's just as often imaginary as it is real. You could ask the same thing about birds. What are birds? We just don't know. Complex numbers are part of the add-on package for mathematics. In this set, the real axis has a new friend, called the imaginary axis. According to linear algebra, these make out a two-dimensional subsphere called the complex add-on package sphere ball thingy. Every point on the surface on previously mentioned whatever is defined to be a complex number, denoted by z (or a, b, ... or any other symbol, really).
- where are real numbers and is the imaginary unit. The set of complex numbers, denoted C or , is a field under the operations of addition, multiplication, and exponentiation defined as follows: This means that these complex-number operations are commutative, associative and distributive in the same way as their real-number counterparts. Note that the final expression above is the result of multiplying out the left hand side in the usual way (using the FOIL method) and simplifying using the fact that (see Imaginary unit). It is easily seen that all real numbers are also complex numbers, since All purely imaginary numbers are also complex, since The complex numbers can also be thought of as a two-dimensional vector space over the real numbers, with basis vectors 1 (one, the real unit) and (the imaginary unit). In this case, a complex number may be written as:
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