Identity true in the reals, not in complex?

[Char. Limit]

Are there any identities that are true for all real numbers, but not for all complex numbers? The only one I can think of is...

$$\sqrt{ab}=\sqrt{a}\sqrt{b}$$

Which is only true if a and b are POSITIVE, not real. But is there any identity that works for all real numbers, but fails for complex numbers?

 

[Hurkyl]

The most obvious is Re(x) = 0.

 

[CRGreathouse]

$$x^2\neq-1$$

 

[Hurkyl]

The most obvious is Re(x) = 0.

And, of course, by Re I mean Im.

 

[losiu99]

Pretty much all the formulas concerning multivalued functions must be treated with caution.

 

[Bill Simpson]

For all x,y x<y or x=y or x>y

 

[Mentallic]

For all x,y x<y or x=y or x>y

Inequalities aren't allowed in the complex field, but equalities are.

 

[CRGreathouse]

|x| != |y| => x = -y

 

[fourier jr]

the law of trichotomy

 

[fourier jr]

I don't know that it's the same thing as the OP asks but cauchy's integral formula is something else that's different. the value of a real function doesn't have anything to do with the value of its derivative but with complex functions it does.