How to graph the complex function z^2 + z*^2 = 2?

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SUMMARY

The discussion focuses on graphing the complex function defined by the equation z² + z'² = 2, where z represents a complex number expressed as z = x + yi and z' denotes its conjugate. The equation simplifies to x² = 2, indicating that the real part of z can take values of ±√2. Participants clarify terminology, emphasizing that "conjugate" is the correct term rather than "complement." The conversation highlights the need for accurate mathematical language in complex analysis.

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z^2 +z'^2=2
' means complement
z=x+yi

i got x^2=2

so howto describe that on real complex graph
?
 
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lom said:
z^2 +z'^2=2
' means complement
z=x+yi

i got x^2=2

so howto describe that on real complex graph
?
I don't get x2 = 2. Also, the term is "conjugate" not "complement."
 

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