The discussion revolves around the problem of sketching the modulus of a complex function, specifically \(|\frac{z+1}{2z+3}|=1\), where \(z=x+iy\). Participants are exploring how to simplify the resulting equation into the standard form of a circle.
The conversation is ongoing, with participants providing insights into algebraic manipulation and expressing their struggles with the completion of the square. There is a recognition of the need for further clarification on the specific difficulties encountered.
Participants are working under the constraints of homework rules, which may limit the extent of guidance provided. The original poster expresses uncertainty about the simplification process, indicating a need for foundational understanding in manipulating quadratic equations.
Keshroom said:i'm stuck at
0= 3x^2 + 3y^2 + 10x + 8
I usually complete the square on these type of problems but it has a 3x^2. What can i do to get it to the form of a circle?
That's what you want to do. What specifically is it about completing the square that is a problem for you?Keshroom said:Homework Statement
Sketch modulus((z+1)/(2z+3))=1 on the complex plane where z=x+iy
Homework Equations
The Attempt at a Solution
I know it is a circle but i need help simplifying the equation into the form of a circle.
i'm stuck at
0= 3x^2 + 3y^2 + 10x + 8
I usually complete the square on these type of problems but it has a 3x^2. What can i do to get it to the form of a circle?
DeIdeal said:If you want to complete the square but can't because of the 3x2 there, what can you do to remove the 3? Divide by it!