Argand diagrams and modulus-argument formAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

What is |x+iy|?
What is the range of the principal argument?
Write z in modulus-argument form.
What are \arg(-1), \arg(i) and \arg(-i)?
State the rule for |z1z2| and \arg(z1z2).
State the rule for \left|\frac{z1}{z2}\right| and \arg\frac{z1}{z2}.
Which results prove the multiplication rule?
What does multiplying by i do on an Argand diagram?
What does conjugation do on an Argand diagram?
What complex number is the vector from P (representing p) to Q (representing q)?
Find \arg(-3+3i).
What is the first step in finding an argument?

Exam questions on Argand diagrams and modulus-argument form

The complex number $z=-1+i\sqrt3$ .
Use the modulus-argument form of $z$ to find $z^3$ .2 marks
The complex numbers $z_1$ and $z_2$ are given by $z_1=\sqrt3+i$ and $z_2=1+i$ .
Find $\arg\left(\frac{z_1}{z_2}\right)$ , in radians.2 marks
On an Argand diagram the points $A$ and $B$ represent the complex numbers $z=3+4i$ and $iz$ respectively, and $O$ is the origin.
Find the complex number represented by $B$ in the form $x+iy$ , and show that $OA=OB$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).