1.13 Complex numbers: polar and exponential formsIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

How do you find |z| for z=a+bi?
What is the polar form of z?
State Euler's formula.
What is the exponential form of z?
Principal argument range?
Polar form of -1+\sqrt3\,i?
How do you multiply r1e^{i\theta1} and r2e^{i\theta2}?
How do you divide r1e^{i\theta1} by r2e^{i\theta2}?
What is \left(re^{i\theta}\right)^n for an integer n?
Geometrically, what does multiplying by re^{i\theta} do?
Geometrically, what is z1+z2?
Write a\cos(\omega t+\phi) using a complex number.
How do you add a1\cos(\omega t+\phi1) and a2\cos(\omega t+\phi2)?

Exam questions on 1.13 Complex numbers: polar and exponential forms

The complex number $z=-1+\sqrt{3}\,i$ .
Write $z$ in the form $re^{i\theta}$ , with $\theta$ in radians.2 marks
$z_1=3e^{\frac{\pi}{4}i}$ and $z_2=2e^{\frac{\pi}{12}i}$ .
Describe fully the single geometrical transformation of the Argand diagram that maps $z_1$ to $z_1z_2$ .2 marks
The complex number $w=1+i$ .
Write $w$ in the form $re^{i\theta}$ and hence find $w^{10}$ in the form $a+bi$ .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).