QCEVault

Further complex numbers — Question 186

Original QCE Vault practice · 5 marks

Q186 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 186 (5 marks)

The polynomial p(z)=z3+az2+bz+10p(z)=z^3+az^2+bz+10 has real coefficients a,b and zero 1+i1+i.
a)
Determine a and b.
[3 marks]
b)
Determine the remaining zeros and explain why no further zeros are possible.
[2 marks]
Question linkSyllabus coverage

Related questions

  1. Q148 · Original practice · 1 mark
    The four roots of z4=−16z^4=-16 are shown on the Argand plane. For each root, a new complex number is defined by
    w=z+4z.w=z+\frac{4}{z}.
    Which statement describes the set of distinct values of ww?
    Further complex numbers
  2. Q153 · Original practice · 1 mark
    The points AA, BB and CC represent the three roots of z3=−8iz^3=-8i on the Argand plane. The point PP represents z=2z=2. What is the exact value of PA×PB×PCPA\times PB\times PC?
    Further complex numbers
  3. Q173 · Original practice · 5 marks
    Four beacons in a light installation have complex coordinates given by the solutions of (z−1−i)4=16(z-1-i)^4=16. They are represented on the Argand plane. The dashed circle has centre C=1+iC=1+i.
    Further complex numbers
  4. Q174 · Original practice · 8 marks
    A nonzero complex number satisfies ∣z∣=1|z|=1. Define w=z+1/zw=z+1/z.
    Further complex numbers