imaginary
1
9.9
- noun
- /ɪˈmædʒɪˌnɛri/
- Specialized
:
número imaginario
- Just as real numbers form a "number line," complex numbers form a "number plane," traditionally drawn such that the pure real numbers are along the horizontal axis and the pure imaginaries are along the vertical axis.
Examples
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The number 5 + 3<i>i</i> includes an imaginary part, which contributes to its complex nature.
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Complex numbers have an imaginary unit but also a real part.
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Now if this was the complex plane, this would be the real axis, and this would be the imaginary axis.
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So engineers, instead of using the letter lowercase I for the imaginary unit, they used J, which is really quite interesting.
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So here's the again, real axis and the imaginary axis.
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You could rewrite it as D MU Phi real squared plus D MU Phi imaginary squared.
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Instead of real numbers and imaginary numbers, we've got watts, which is real power, and Volt amps, which is reactive power on the Y axis here.
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In the equation, the imaginary part is represented as imaginary and is multiplied by the square root of -1.
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In complex number theory, an imaginary component is essential for defining certain mathematical concepts.
Synonyms
1
7.9
A number in the form a plus b i, where i is the square root of minus one
1
6.3
A number with a real part and an imaginary part written as a + bi
A number with one real part and one imaginary part
Compounds
- Specialized
1
7.9
A number in the form a plus b i, where i is the square root of minus one
- Specialized
The number you multiply by i in a complex number, for example 3 in 5 + 3i
- Specialized
A number equal to a real number not zero times i with no real part
Surface Forms
Morphology
imaginary = imagine (opaque) = imagin + ary
The form is a regular derivation from imagine + -ary, with only a minor spelling reduction in the stem.
Etymology
Imaginary for numbers comes from the same root as imagine and image, meaning something made by the mind, and mathematicians called numbers that are not 'real' 'imaginary', so an imaginary number is easy to remember as not a 'real' number.