Can we set a sequence to the imaginary numbers?

We cannot set a sequence to the imaginary numbers because

1. Set $i > 0$ . Then $i^{2} > 0i \rightarrow -1 > 0$ .

$-1$ cannot be bigger than $0$ so $i$ is not bigger than 0.

1. Next, set $i < 0$ . Then $i^{2} > 0i \rightarrow -1 > 0$ .

We found a wrongness again as 1, so $i$ is not smaller than 0.

1. Finally, set $i = 0$ . Then $i^{2} = 0i \rightarrow -1 = 0$ .

$-1$ cannot be equal to $0$ , thus we cannot set a sequence to the imaginary numbers.

So we cannot know if $i$ is bigger, smaller, or equal than $0$ .

And of course, our steps are all wrong because, in whole real numbers, we square it, then it must be equal or bigger than $0$ , but we can found the number which is getting squared, it becomes negative when we are solving quadratic equations, cubic equations, etc.

Like $3x^{2} - 5x + 4 = 0 \Rightarrow \frac{ 5 \pm \sqrt{ 25 - 4 \times 3 \times 4 }}{ 2 \times 3 } \Rightarrow \frac{ 5 \pm \sqrt{ 25 - 48 }}{ 6 } \Rightarrow \frac{ 5 \pm \sqrt{ -13 }}{ 6 } \Rightarrow \frac{ 5 \pm \sqrt{ 13 }i }{ 6 }$ .

So we cannot set a sequence to the imaginary numbers.