Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: $\frac{1 - i}{1 + i}$

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Solution

$\frac{1 - i}{1 + i} = \frac{(1 - i)^{2}}{1^{2} - i^{2}} = \frac{1 - i^{2} - 2 i}{2} = - i = e^{i \frac{3 π}{2}}$
Modulus and argument of $\frac{1 - i}{1 + i}$ are $1$ and $\frac{3 π}{2}$ respectively

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Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: $\frac{1 - i}{1 + i}$

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