x̄ - > Proof that no order can be defined in the complex field that turns it into an ordered field.

Complex Numbers 

Expressed in the form a+bi where a and b are real numbers and I an imaginary part where
 i^2 =-1.

Prove that no order can be defined in the complex field that turns it into an ordered field.  

Any squares ordered fiel squares are greater than or equal to 0

which means0=1 a contradiction 

z = a + bi  , and w = c + di. z < w,a < c,,a = c,b < d

proof??????? 

Since i^2 = −1, this means that 0 ≤ −1Thus1 = 0 + 1 ≤ −1 + 1 = 0 ≤ 1, which implies 0 = 1, a contradiction.Solved

To show the values of  r and ⊝(polar coordinates)

Formulas_and_Tables_Shaums-Read-Only

Let z=3+4i which can also be written in the form z=re^i⊝.
Let Coordinates x=rcos⊝
                              Y=rSin⊝
Recall Tan⊝=Sin⊝/Cos⊝
Knowing 3=x .and 4=Y then
                  3=rcos⊝  and 4=rsin⊝
Tan⊝ would be 4/3 or rsin⊝/rcos⊝
Arctan⊝(4/3)=⊝
And 5=r

• Solved 

Solve z=2e^iπ/4

Recall x=rcos⊝

 Y=rSin⊝
e^i⊝=cos⊝ + isin⊝
Then
2e^iπ/4=2cosπ/4+2isinπ/4
cosπ/4= 1/2√2 and sinπ/4=1/2√2

 z=2e^iπ/4=√2+i√2 

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