Complex numbers order

Do complex numbers have order?
TL;DR: The complex numbers are not an ordered field ; there is no ordering of the complex numbers that is compatible with addition and multiplication.
If a structure is a field and has an ordering , two additional axioms need to hold for it to be an ordered field._{Mar 30, 2016}.
Is there order in complex numbers?
The complex numbers can be ordered.
It cannot be made into an ordered field with the usual addition and multiplication._{Nov 21, 2014}.
What is the order of complex numbers?
TL;DR: The complex numbers are not an ordered field ; there is no ordering of the complex numbers that is compatible with addition and multiplication.
If a structure is a field and has an ordering , two additional axioms need to hold for it to be an ordered field._{Mar 30, 2016}.
What order is a complex number written?
We use 5i and not −5i because the principal root of 25 is the positive root.
A complex number is the sum of a real number and an imaginary number.
A complex number is expressed in standard form when written a+bi where a is the real part and bi is the imaginary part.
For example, 5+2i is a complex number..
Why are complex numbers unordered?
1 Answer.
Suppose, i\x26lt;0, then since multiplying with a negative number changes the sign, we have i2\x26gt;0, again a contradiction.
So, neither i\x26gt;0 nor i\x26lt;0 is consistent with the rules of ordered numbers..
Therefore, an imaginary number is the part of complex number which we can write like a real number multiplied by the imaginary unit i, where i² = -1.
The imaginary number, when multiplied by itself, gives a negative value.

Nov 21, 2014The complex numbers can be ordered. It cannot be made into an ordered field with the usual addition and multiplication.Total ordering on complex numbers - Mathematics Stack ExchangeImpossibility of ordering the complex numbersWhy the complex number system is not an ordered field [duplicate]Ordering on complex numbers - Mathematics Stack ExchangeMore results from math.stackexchange.com

Nov 21, 2014The complex numbers can be ordered. It cannot be made into an ordered field with the usual addition and multiplication.Total ordering on complex numbers - Mathematics Stack ExchangeWhy the complex number system is not an ordered field [duplicate]Impossibility of ordering the complex numbersOrdering on complex numbers - Mathematics Stack ExchangeMore results from math.stackexchange.com

Complex numbers order

Do complex numbers have order?

Is there order in complex numbers?

What is the order of complex numbers?

What order is a complex number written?

Why are complex numbers unordered?