Question

The modulus and amplitude of $\frac{1+2i}{1-(1-i{)}^2}$ are ____

• A. $\sqrt{2}$ and $\frac{\pi }{6}$
• B. 1 and $\frac{\pi }{6}$
• C. 1 and 0
• D. 1 and $\frac{\pi }{3}$

Answer 1

The correct option is C 1 and 0

Given that: $\frac{1+2i}{1-(1-i{)}^2}$
$=\frac{1+2i}{1-(1-2i-1)}$
$=\frac{1+2i}{1-(-2i)}$
$=\frac{1+2i}{1+2i}$
$=1$
$=e^{i0}$
Hence modulus is 1 while amplitude is 0.