Question

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

• A. $\frac{-\pi }{2}$ and 1
• B. $\frac{\pi }{2}$ and $\sqrt{2}$
• C. 0 and $\sqrt{2}$
• D. $\frac{\pi }{2}$ and 1

Answer 1

Answer: (D)

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