Edexcel A Level Further Maths
Topic questions Pure mathematics Complex roots of equations
9 questions · 73 marks · about 1.5 hours
f (z) = z3 + az2 + bz + c where a, b and c are real constants
The roots of the equation f (z) = 0 are z1, z2 and z3
When plotted on an Argand diagram, the points representing these roots form the vertices of a triangle.
Given that
• z1 
2 
4i
• the area of the triangle is 12
Determine the two possible functions f (z)
f(z) = z4 
6z3 
az2 bz 
145
where a and b are real constants.
Given that 2 + 5i is a root of the equation f(z) = 0
determine the other roots of the equation f(z) = 0
Show all the roots of f(z) = 0 on a single Argand diagram.
f(z) = z4 6z3 az2 bz 145
where a and b are real constants.
Given that 2 + 5i is a root of the equation f(z) = 0
determine the other roots of the equation f(z) = 0
Show all the roots of f(z) = 0 on a single Argand diagram.
f(z) = z3 + az + 52 where a is a real constant
Given that 2 – 3i is a root of the equation f(z) = 0
write down the other complex root.
Hence
solve completely f(z) = 0
determine the value of a
Show all the roots of the equation f(z) = 0 on a single Argand diagram.
f(z) = z3 + az + 52 where a is a real constant
Given that 2 – 3i is a root of the equation f(z) = 0
write down the other complex root.
Hence
solve completely f(z) = 0
determine the value of a
Show all the roots of the equation f(z) = 0 on a single Argand diagram.
f (z) = 3z3+pz2+ 57z+q
where p and q are real constants.
show all the roots of f(z) = 0 on a single Argand diagram,
find the value of p and the value of q.
f (z) = 3z3+pz2+ 57z+q
where p and q are real constants.
show all the roots of f(z) = 0 on a single Argand diagram,
find the value of p and the value of q.
where a, b, c and d are real constants.
Given that í1 + 2i and 3 í i are two roots of the equation f (z
=show all the roots of f (z) = 0 on a single Argand diagram,
find the values of a, b, c and d.
where a, b, c and d are real constants.
Given that −1 + 2i and 3 − i are two roots of the equation f (z) = 0
show all the roots of f (z) = 0 on a single Argand diagram,
find the values of a, b, c and d.
Memes
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