Question
Sun September 29, 2013 By:
 

if |a+ib|=1 then show that : (1+b+ai)/(1+b-ai)= b+ai.

Expert Reply
Mon September 30, 2013
here |a+bi|=1
so a^2+b^2=1
(1+b+ai)/(1+b-ai)
using concept of rationalization
(1+b+ai)^2/(1+b)^2+a^2
=1+b^2+2b-a^2+2ai(1+b)/(1+b^2+2b+a^2)
using a^2+b^2=1
2b^2+2b+2ai(1+b)/2(1+b)
=(1+b)(b+ai)/(1+b)
=b+ai
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