Imaginary Number

An Imaginary Number is a Number that is based on a real number multiplied by an imaginary unit.

• • …
• Example(s):
  • [math]\displaystyle{ 2 i }[/math].
  • [math]\displaystyle{ \pi i }[/math].
  • …
• Counter-Example(s):
  • a Real Number.
• See: Complex Number, Imaginary Unit, Square (Algebra), Real Part, Modular Arithmetic.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Imaginary_number Retrieved:2014-10-16.
  • An imaginary number is a number that can be written as a real number multiplied by the imaginary unit , which is defined by its property . The square of an imaginary number is . For example, is an imaginary number, and its square is . Except for 0 (which is both real and imaginary ), imaginary numbers produce negative real numbers when squared. An imaginary number can be added to a real number to form a complex number of the form , where the real numbers and are called, respectively, the real part and the imaginary part of the complex number. Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. The term "imaginary number" now means simply a complex number with a real part equal to, that is, a number of the form .

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