Question 1420b

Complex Numbers
2020 Paper 1 Question 6 Variant

Question

The complex number z{z} satisfies the equation
z2(1+5i)+(7+11i)z+t=0, z^2(1 + 5 \mathrm{i}) + (- 7 + 11 \mathrm{i})z + t = 0,
where t{t} is a real number. It is given that one root is of the form k+ki,{k + k \mathrm{i},} where k{k} is real and non-zero.
Find t{t} and k,{k,} and the other root of the equation.
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Answer