1.12 Complex numbers: Cartesian formIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

Define i.
Cartesian form of a complex number?
Real and imaginary part of 3+4i?
Conjugate of a+bi?
Modulus of a+bi?
What is the argument of z?
How do you divide complex numbers?
Simplify (3+4i)(1-2i).
What is z\,z^{}?
What do the axes of an Argand diagram show?
What does b^{2}-4ac<0 tell you?
Solve x^{2}-6x+25=0.

Exam questions on 1.12 Complex numbers: Cartesian form

Let $z=3+4i$ and $w=1-2i$ .
Find $\frac{z}{w}$ , giving your answer in the form $a+bi$ .2 marks
Let $u=2-3i$ and $v=4+i$ .
Use your GDC to find $u^{4}$ .2 marks
Consider the quadratic equation $x^{2}-6x+25=0$ .
Show that the equation has no real solutions.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).