If a, b, c are non-zero real number with c 1 such that a^2+b^2+c^2=c and if = a+i b 1-c , then a^2+b^2=

Step-by-step solution

Given that, = a+i b 1-c | |^2= a^2+b^2 (1-c)^2 And a^2+b^2+c^2=c a^2+b^2=c(1-c) From Eqs. (i) and (ii), aligned & | |^2= c (1-c) 1+| |^2 1 = 1 1-c 1-c & = 1 1+| |^2 aligned From Eqs. (i) and (iii), we get | |^2= a^2+b^2 ( 1 1+| |^2 )^2 a^2+b^2= | |^2 (1+| |^2 )^2