Complex Numbers - Arithmetic with Complex Numbers in Cartesian Form
Complex Numbers - Arithmetic with Complex Numbers in Cartesian Form
If \(z=\dfrac{2-i}{1+3i}\), find the real and imaginary parts of \(z-\dfrac1z\).
Hence, find all complex numbers \(w\) in Cartesian form such that \(w-\dfrac1w=\dfrac1{10}+\dfrac{21}{10}i\).
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Answer:\(\operatorname{Re}(z-1/z)=\tfrac1{10},\ \operatorname{Im}(z-1/z)=-\tfrac{21}{10}\). \(w=-\tfrac1{10}+\tfrac7{10}i\) or \(w=\tfrac15+\tfrac75i\).
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