Paper 1, Section I, 1C1 \mathrm{C}

Vectors and Matrices | Part IA, 2013

(a) State de Moivre's theorem and use it to derive a formula for the roots of order nn of a complex number z=a+ibz=a+i b. Using this formula compute the cube roots of z=8z=-8.

(b) Consider the equation z+3i=3z|z+3 i|=3|z| for zCz \in \mathbb{C}. Give a geometric description of the set SS of solutions and sketch SS as a subset of the complex plane.

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