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Complex numbers are numbers of the form $a+bi$ where $a$ and $b$ are both real numbers. Pure imaginary numbers, on the other hand, are complex numbers of the form $a+bi$ where $a=0$ and $b\ne0$. Therefore, pure imaginary numbers are a subset of the set of complex numbers. This means that every pure imaginary number is a complex number while every complex number may not be a pure imaginary number.