Imaginary unit

English

the complex or Cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis.

Etymology

So named because it takes on the role of unit for the imaginary part of a complex number.

Noun

1. Template:Lb An imaginary number (in the case of complex numbers, usually denoted $i$) that is defined as a solution to the equation $x^2=-1$.
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   • 2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Template:W), 5th Edition, page 793,

     We now simply say that $i$ is the imaginary unit and define it by the property $i^2=-1$. Using the imaginary unit, we build a general complex number out of two real numbers.

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Usage notes

• The imaginary unit of complex analysis is usually denoted $i$. In some fields (for instance, electrical engineering), however, it is customarily denoted $j$, to avoid confusion with the symbol for electric current.
• The complex numbers are generated by assuming a single imaginary unit, $i$, and constructing the numbers $a+bi$, where $a$ and $b$ are real numbers.
• The quaternions (regardable as an extension of the complex numbers) are similarly generated by assuming three distinct imaginary units, $i,j,k$, and constructing the numbers $a+bi+cj+dk$.

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