Complex Numbers - Representing Complex Numbers on an Argand Diagram
Complex Numbers - Representing Complex Numbers on an Argand Diagram
TGM Original Questions
The point \(P\) represent the complex number \(z=3-4\mathbf{i}\). Let the points \(Q\), \(R\) and \(S\) represent the complex numbers \(\mathbf{i}z\), \(-z\), \({{z}^{*}}\) respectively.
- Describe the geometric transformations that map the point \(P\) to the points \(Q\), \(R\) and \(S\).
- Hence represent the points \(P\), \(Q\), \(R\) and \(S\) on a single argand diagram, clearly illustrating their relationship.
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:\(\text{(a)}\ Q:4+3\mathbf{i}\text{, rotation by}\hspace{0.5em}\dfrac{\pi}{2};\ R:-3+4\mathbf{i}\text{, rotation by}\hspace{0.5em}\pi;\ S:3+4\mathbf{i}\text{, reflection in the real axis}\) \(\text{(b)}\ P(3,-4),\ Q(4,3),\ R(-3,4),\ S(3,4);\ |z|=5\)
Need help? Join our JC Math tuition classes.
Learn more