Sketch, on an Argand diagram, the locus of points representing the complex number \(z\) such that \(|z+2-3\mathrm i|=\sqrt{13}\).[3]
The complex number \(w\) is such that \(ww^*+2w=3+4\mathrm i\), where \(w^*\) is the complex conjugate of \(w\). Find \(w\) in the form \(a+\mathrm ib\), where \(a\) and \(b\) are real.[4]
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Answer:(a) Circle centre \((-2,3)\), radius \(\sqrt{13}\). (b) \(-1+2\mathrm i\).