Question
Let .
Solve .
[5]
a.
Show that .
[3]
b.
Find the modulus and argument of in terms of . Express each answer in its simplest form.
[9]
c.i.
Hence find the cube roots of in modulus-argument form.
[5]
c.ii.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
(M1)(A1)
A1
M1
A1
[5 marks]
a.
EITHER
choosing two appropriate angles, for example 60° and 45° M1
and
(A1)
A1
AG
OR
attempt to square the expression M1
A1
A1
AG
[3 marks]
b.
EITHER
M1
A1
A1
A1
let
M1
(A1)
A1
A1
A1
OR
M1A1
(A1)
M1A1
M1A1
A1
A1
[9 marks]
c.i.
attempt to apply De Moivre’s theorem M1
A1A1A1
Note: A1 for modulus, A1 for dividing argument of by 3 and A1 for .
Hence cube roots are the above expression when . Equivalent forms are acceptable. A1
[5 marks]
c.ii.
Examiners report
Syllabus sections