Question

Find the modulus of $\frac{1+i}{1-i}$.

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

Answer: (A)

Let $z=\frac{1+i}{1-i}$
$\therefore \left|z\right|=\left|\frac{1+i}{1-i}\right|=\frac{|1+i|}{|1-i|}$
$=\frac{\sqrt{1^2+1^2}}{\sqrt{1^2+1^2}}=\frac{\sqrt{2}}{\sqrt{2}}$
$=1$