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The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.. The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0.
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A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi, whose real part is zero. It is common to write a + 0i = a, 0 + bi = bi, and a + (−b)i = a − bi; for example, 3 + (−4)i = 3 − 4i.
This image is a derivative work of the following images: Image:Imaginarynumber2.PNG licensed with GFDL . 2007-01-30T02:12:11Z Mets501 265x220 (4077 Bytes) An illustration of a complex number plotted on the complex plane.
An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
For example, in the Flash Anzan event at the All Japan Soroban Championship, champion Takeo Sasano was able to add fifteen three-digit numbers in just 1.7 seconds. [ 2 ] This system is being propagated in China, [ 3 ] Singapore, South Korea, Thailand, Malaysia, and Japan.
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
IMAGINARY was founded at the Mathematisches Forschungsinstitut Oberwolfach (MFO) in 2007 by Gert-Martin Greuel and Andreas Matt with an exhibition of the same name, supported by Klaus Tschira Foundation. In 2013 Gert-Martin Greuel and Andreas Matt received the Media Prize Mathematics of the German Mathematicians Association for IMAGINARY. [1]