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1. a) Express z = −i−sqrt(3) in the form r cis θ, where θ= Argz, and...

1.

a)
Express z = −i−sqrt(3) in the form r cis θ, where θ= Argz, and then use de Moivre’s theorem to find the two square roots of −4i.

b) Consider:
i) p(z)=iz^2+z^3+2iz−2z^2+2z. Given that z=2−2i is a zero of this polynomial, find all of its zeros.
ii) p(z)=z^3−2z^2+9z−18. Factorise into linear factors.
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