Why $i^2=-1$ in complex numbers?

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Why do we use specifically iota (where $i^2=-1$) in complex numbers? Complex numbers are used in multi-dimensional applications. But we can also use any symbolic term in place of $i$. Why do we use specifically iota? What is the link between the equation $i^2=-1$ and Argand diagram?

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My guess is that it is $i$ for imaginary, that is what I was always told.