If $z=\dfrac{1-\mathbf{i}}{2+\mathbf{i}}$, find the real and imaginary part of \(z-\dfrac{1}{

Question

If $z=\dfrac{1-\mathbf{i}}{2+\mathbf{i}}$, find the real and imaginary part of $z-\dfrac{1}{z}$. Hence, find the complex number $w$ in Cartesian form such that $w-\dfrac{1}{w}=-\dfrac{3}{10}+\dfrac{21}{10}\mathbf{i}$.

Accepted Answer

Real part =$-\frac{3}{10}$, Imaginary =$-\frac{21}{10}$; $w=\frac{1}{5}+\frac{3}{5}\mathbf{i}$

Complex Numbers - Arithmetic with Complex Numbers in Cartesian Form

Complex Numbers - Arithmetic with Complex Numbers in Cartesian Form

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