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Imaginary number

An imaginary number has no real value. You write it as

i y

where i is the imaginary unit.



Imaginary numbers are part of a complex number, that is denoted by the letter as

z = x + iy

where x and y are real numbers, and i de imaginary unit. A complex number has a real part and an imaginary part. You can say that iy is an imaginary number, but it is also a complex number, because

z = 0 + iy

And i itself is also a complex number, because

i = 0 + 1i

it consists only of an imaginary part. It has no real value. Every real number is a complex number, because

x = x + 0i

The name 'imaginary number' is not widely used in practice. Sometimes you find 'imaginary pure' instead. It always describes the imaginary part of a complex number. They can be found in exponential functions and then the distinction is not important. There you get

where each term can be handled separately.


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