Moderate -0.5 This is a standard locus question requiring students to translate a modulus equality into Cartesian form. The method is routine: substitute z = x + iy, expand both moduli using √[(x-a)² + (y-b)²], square both sides, and simplify. The algebra is straightforward and leads directly to a linear equation. This is easier than average as it's a textbook exercise with a well-practiced technique and minimal problem-solving required.
6. The complex number \(z\) is represented by the point \(P ( x , y )\) in an Argand diagram.
Given that
$$| z - 1 | = | z - 2 \mathrm { i } |$$
show that the locus of \(P\) is a straight line.
6. The complex number $z$ is represented by the point $P ( x , y )$ in an Argand diagram.
Given that
$$| z - 1 | = | z - 2 \mathrm { i } |$$
show that the locus of $P$ is a straight line.\\
\hfill \mbox{\textit{WJEC Further Unit 1 2019 Q6 [3]}}