Question 1

Paper 1, no calculatorMedium7 marks

Consider the equation

z3=8(cos⁡π+isin⁡π).z^3=8(\cos\pi+i\sin\pi).
(a)

Determine all distinct solutions, giving each in the form a+bia+bi

[4]
(b)

Hence determine the monic quadratic polynomial with real coefficients whose roots are the two non-real solutions of the equation.

[3]

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