Hi everyone my name is Sany and welcome to
My Maths Adventure. In this video I'll be giving you a review of
Argand diagrams, the second chapter of the A Level Further Maths
Core Pure 1 book.
Argand diagrams is the second chapter of the Pearson
Edexcel Core Pure 1 Further Maths book. It was interesting to see how Complex
numbers are applied to the x, y plane and also the applications that you
could achieve by seeing imaginary numbers plotted.
The Argand diagram takes your understanding of
Complex numbers from the first chapter and applies it
geometrically. In my first video in this series on
A Level Further Mathematics, I said that z equals a plus b i.
In this chapter we'll change it up a little bit by saying that
z equals x plus y i instead as we are now working in the complex plane.
There's no difference just a change of terminology. Now there are five
main sections in this chapter. The first three sections
I really enjoyed, however when I got to loci
sections then that's when things got really challenging.
Now there are many ways that loci can be represented on an Argand diagram.
I can see why imaginary numbers can be so important in perhaps mechanical
engineering because some of these diagrams looks
like they can be applied to the real world.
Now the key skills that you will need to know beforehand are
coordinate geometry in the x y plane, to include
finding the gradient equation length and midpoint of a line,
the equations of lines which are parallel or perpendicular
to a given line, the equation of a circle finding the centre given a point and
radius, knowledge of radians, understand and use
the modulus function, understand and use the trigonometric
addition formulae, be able to interpret and sketch
inequalities and strong graph sketching skills. From my
study experience I think that this chapter will require you to have
strong coordinate geometry skills from the first year
of your A Level Mathematics. Co ordinate geometry is ubiquitous
across all the exam boards in the uk. It's in the first year of your A Level
mathematics study and one whole chapter in your textbook
is dedicated to it. Nothing can be skimmed over because all
the skills you learn in that chapter are essential, as you will need to learn them
to solve problems in the Argand diagram. Don't gloss over
the section on circles either in the coordinate
geometry section. You'll need those circle skills to be
able to do the loci exercises in this section. Now there are
key skills that you would need to know beforehand
that aren't taught until the second year of your A Level mathematics course.
These subjects are radians, the modulus function
and the trigonometric addition formulae. If you're studying the first year of
your A Level mathematics course alongside the first year of your Further
Maths course, then it will be challenging as those
skills won't be taught until the second year of your normal
A Level maths course. My advice is to do some pre-study before
you start this chapter. It's essential that you understand the
modulus function and radians as they are important
elements of the modulus argument of a complex number. The trig
addition identity also plays an important part in being
able to manipulate equations in complex form. Looking at the
specification the topics that will be covered in this chapter
are: news and interpret Argand diagrams, understand a news cartesian and modulus
argument forms of a complex number, convert between cartesian form and the
modulus form of a complex number, multiply and divide complex numbers in
modulus argument form and construct and
interpret simple loci in the Argand diagram.
As I mentioned before when you get to loci section it can get
really challenging you need a strong imagination
to conceptualise the mathematical geometric diagrams.
That's why good graph sketching skills is so important in this chapter.
The ability to represent geometric interpretations
of equations is sometimes a neglected skill
in mathematics because as Maths students, we don't get an opportunity
to practice it much. Working in the complex plane will sometimes require you
to draw a circle with a certain centre and radius. You may
have to sketch lines that may meet the circle either at
the centre at a certain point or at a tangent.
Then as a further challenge you may have to sketch angles measured in radians
within that diagram as well. In summary the Argand diagram chapter will extend
your learning about complex numbers and will apply it to the x, y plane. It's
a demanding chapter that will bring together the core coordinate geometry
and trigonometry skills from your first year A Level maths
and key parts of the second year of your A Level maths syllabus as well.
Now there is an excellent video by Mrs O'Gram's Maths where she gives a brief
introduction to elements that you'll be studying
in this chapter on Argand diagrams. The video is a great way to get a flavour of
what you'd be studying in this section and the skills that you will need
I'll link the video in the description above. The next
chapter I'll be reviewing is Series. Definitely a shorter chapter
compared to the last two and we'll perhaps give you a short
breather after these two challenging chapters on Complex numbers and Argand
diagrams. Hopefully you can join me in the next
video on this A Level Further Mathematics
review series