9709 P3 - Jun 2007 - Q8
1908
The complex number \(\frac{2}{-1+i}\) is denoted by \(u\).
(i) Find the modulus and argument of \(u\) and \(u^2\).
(ii) Sketch an Argand diagram showing the points representing the complex numbers \(u\) and \(u^2\). Shade the region whose points represent the complex numbers \(z\) which satisfy both the inequalities \(|z| < 2\) and \(|z-u^2| < |z-u|\).
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