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 ?!!

#Algebra

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Comments

$\sqrt{-1}$ 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.

Guilherme Dela Corte - 6 years, 11 months ago

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

Kïñshük Sïñgh - 6 years, 11 months ago

will, but in simple other words is 5i>4i or 5i<4i or that's impossible !

Peace Trap - 6 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$