An imaginary number is a complex number in which the real part is zero and the imaginary part is non-zero. It is typically written in the form $bi$, where $b$ is a real number and $i$ denotes the imaginary unit, defined as $i = \sqrt{-1}$.
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Imaginary numbers are used to extend the real number system to solve equations that have no real solutions, such as $x^2 + 1 = 0$.
The basic unit of imaginary numbers is $i$, where $i^2 = -1$.
Any complex number can be written as a sum of a real and an imaginary number: $a + bi$.
Operations with imaginary numbers follow similar rules to those for real numbers but include the additional property that $i^2 = -1$.
Imaginary numbers are plotted on the vertical axis of the complex plane, while real numbers are plotted on the horizontal axis.
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Related terms
Complex Number: A number that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.
Real Number: A value representing a quantity along a continuous line, including all rational and irrational numbers.
$i (Imaginary Unit)$: $i$ is defined as $\sqrt{-1}$, and it satisfies the equation $i^2 = -1$. It forms the basis for all imaginary numbers.