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An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. 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.
|All powers of i assume values|
from 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|
Originally coined in the 17th century by René Descartes 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.
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