Paper 1, Section I, C

Vectors and Matrices | Part IA, 2009

Describe geometrically the three sets of points defined by the following equations in the complex zz plane:

(a) zαˉ+zˉα=0z \bar{\alpha}+\bar{z} \alpha=0, where α\alpha is non-zero;

(b) 2za=z+zˉ+2a2|z-a|=z+\bar{z}+2 a, where aa is real and non-zero;

(c) logz=ilogzˉ\log z=\mathrm{i} \log \bar{z}.

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