Edexcel A Level Further Maths
Topic questions Pure mathematics Modulus-argument form
8 questions · 44 marks · about 55 minutes
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Given that
show that
arg(zw) 
arg(z) 
arg(w)
The complex number z = eiθ, where θ is real.
Show that
where n is a positive integer.
Show that
Hence, making your reasoning clear, determine all the solutions of
cos 5 θ + 5 cos 3 θ + 12 cos θ = 0
in the interval 0 
θ < 2π
A student was asked to answer the following:
The student’s attempt is shown below.
The student made errors in line 1 and line 3
Correct the error that the student made in
line 1
line 3
A student was asked to answer the following:
The student’s attempt is shown below.
The student made errors in line 1 and line 3
Correct the error that the student made in
line 1
line 3
Given that
show that
Given that
determine the least value of 
z
as z varies.
Given that
show that
Given that
determine the least value of 
z
as z varies.
Given that
write down the exact value of
|z1z2|
arg(z1z2)
Given that w = z1z2 and that arg(wn) = 0, where n 
+
determine
the smallest positive value of n
the corresponding value of |wn|
Given that
write down the exact value of
|z1z2|
determine
the smallest positive value of n
the corresponding value of |wn|
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