# Imaginary number

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An imaginary number is a real number multiplied by the imaginary unit i,[note 1] which is defined by its property i2 = −1.[1][2] The square of an imaginary number bi is b2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary.[3]

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 All powers of i assume valuesfrom blue area i−3 = i i−2 = −1 i−1 = −i i0 = 1 i1 = i i2 = −1 i3 = −i i4 = 1 i5 = i i6 = −1 i is a 4th root of unity
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Originally coined in the 17th century by René Descartes[4] as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.[5]

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