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complex inequalities

hey, I really want an answer ! do we have inequalities in complex numbers field, or not ? if yes, do we consider i the imaginary number as a positive or negative number ?!!

Note by Peace Trap
2 years, 10 months ago

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No, we don't have inequality in complex nos... Bcz if we try to work upon an inequality... We finally get to know that there is a contradiction... And what we assumed was wrong... Ex..LET # i > i-1 # i² > i² + 1 - 2i # 1/2 < i

That's not possible

:) · 2 years, 10 months ago

$$\sqrt{-1}$$ is not a real number, so we cannot apply definitions of positive and negative numbers.

Suppose $$\sqrt{-1}$$ is negative or positive. Then $$\sqrt{-1}^2$$ will be obviously a positive number. Turns out $$-1 > 0$$ is a false statement, thus the imaginary unit is not negative or positive. · 2 years, 10 months ago