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  4. Argument and modulus of (1+i/1-i) are respectively

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Q. Argument and modulus of $\frac{1+i}{1-i}$ are respectively

Complex Numbers and Quadratic Equations

Solution:

$z=\frac{1+i}{1-i}$
$z=\frac{(1+i)(1+i)}{(1-i)(1+i)}=\frac{1-1+2 i}{2}=i=1 \cdot e^{i \frac{\pi}{2}}$
$\arg (z)=\frac{\pi}{2}$, modulus $=1$