The equation |z - i| = |z + 1| represents the set of points in the complex plane where the distance from the complex number z to the point i is equal to the distance from z to the point -1. This geometric representation is a straight line, specifically the perpendicular bisector of the segment connecting the points i and -1. The discussion clarifies that while |z - i| and |z + 1| can be interpreted as distances, they do not represent circles but rather a linear relationship in the complex plane.
PREREQUISITESMathematicians, students of complex analysis, and anyone interested in the geometric properties of complex numbers will benefit from this discussion.
No, |z - i| represents the distance from an arbitrary complex number z to i. The value is a real number. It is not a circle.lom said:|z-i|=|z+1|
i know that |z-i| is a circle
shifted by i
In your original equation, the expression is |z - 1|. This represents the distance from some complex number z to 1.lom said:|z-1| means center shifted by 1
Think about what it means that the distance from z to i equals the distance from the same z to 1.lom said:but its not telling the full picture