Express in form of a+ib

(1-i)/(1+i)...

Please help me expert......

(1-i)/(1+i)

= (1-i)*(1-i)/(1+i)*(1-i) {Rationalising the denominator}

= (1-i)^{2}/(1^{2}-i^{2})

= (1+i^{2}-2i)/(1^{2}-[-1])

= (1-1-2i)/(2)

= (-2i)/2

= -i

= 0+(-1)i {In the form a+ib where a=0 and b=-1}