Find the modulus and argument of the complex numbers : (i) `(1+i)/(1-i)` (ii) `1/(1+i)`

Explanation

(i) `z = (1+i)/(1-i)**(1+i)/(1+i) = (1+i^2+2i)/(1+1) = i = 0+i`

In polar form,

`r(cos theta + isin theta) = 0+i`

`=> rcos theta = 0 and rsin theta = 1`

`=> r^2(cos^2 theta+sin^2theta) = 0^2+1^2`

`=> r^2 = 1=> r = 1`

Now, `cos theta = 1 => theta = pi/2`

so, modulus is `1` and argument is `pi/2`.


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