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  4. Find the modulus of (1+i/1-i).

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

Complex Numbers and Quadratic Equations

Solution:

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