giải thích chi tiết

To solve the given problem, we can follow these steps: 1. Replace z with x + yi. 2. Use the definition of the conjugate of a complex number: $$. 3. Substitute z and $$ into the equation $$. 4. Simplify the equation and isolate the real and imaginary parts. 5. Express the locus of points in terms of x and y. Here's a detailed explanation using Latex: We start by replacing z with x + yi: $$ Simplify the expression inside the absolute value: $$ Now, let's express 2x + 1 - i in terms of its real and imaginary parts: $$ where a is the real part and b is the imaginary part. Squaring both sides to get rid of the absolute value: $$ Expanding and simplifying: $$ Comparing real and imaginary parts: $$ $$ Solving for a in terms of b from ab=0 gives us two cases: either a=0 or b=0. Case 1: When a=0, we have $$ which gives $$ This has no real solutions, so we discard this case. Case 2: When b=0, we have $$ which gives $$ So, $$ Therefore, combining both cases, we get two lines as loci: When $$, it represents one line, and when $$, it represents another line. Finally, expressing these lines in terms of x and y gives us: The locus of points satisfying $$ is: $$