The discussion focuses on sketching the equation |z - i| = 2 in an Argand diagram, where z is expressed as a complex number z = a + bi. The equation indicates that the distance from the point z to the point i (0, 1) in the complex plane is exactly 2 units. Participants clarify that z can occupy multiple positions around the point i, forming a circle with a radius of 2 centered at (0, 1). The solution emphasizes understanding the geometric interpretation of complex numbers in the Argand diagram.
PREREQUISITESStudents studying complex analysis, mathematics educators, and anyone interested in visualizing complex numbers through Argand diagrams.
Mathematicsss said:Homework Statement
:[/B]
Sketch in an argand diagram:
|z − i| = 2
Homework Equations
z= a+bi
The Attempt at a Solution
|z − i| means that the distance from z to i is 2, however I am not sure where to put z.
There is not just a single location for z -- it is arbitrary. Follow Ray's advice in locating i.Mathematicsss said:|z − i| means that the distance from z to i is 2, however I am not sure where to put z.