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

Vectors and Matrices | Part IA, 2019

(a) If

x+iy=a=0200ia+b=150ibx+i y=\sum_{a=0}^{200} i^{a}+\prod_{b=1}^{50} i^{b}

where x,yRx, y \in \mathbb{R}, what is the value of xyx y ?

(b) Evaluate


(c) Find a complex number zz such that


(d) Interpret geometrically the curve defined by the set of points satisfying

logz=ilogzˉ\log z=i \log \bar{z}

in the complex zz-plane.

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