Thinking@TheCulture is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking Math@TheCulture is curated by KS. More of him can be found here.
(i) Find the two possible values of such that , leaving your answer in exact form , where and are real numbers.
(ii) Hence or otherwise, find the exact roots of the equation
By comparing real and imaginary parts,
Sub into (1)
or (rej since )