If A+ B+ C=0 and A+ B+ C=0 , then (A+B)+ (B+C)+ (C+A) is equal to

Step-by-step solution

Here, we have the pattern of data in x and x , so let's use the method of polar form of complex number. Polar form of complex number, z= +i then z = -i and z z =1 z = 1 z Let z₁= A+i Az₂= B+i B and z₃= C+i C Then, z ₁= A-i A gathered z ₂= B-i B z₃= C- C gathered Now, to find (A+B)+ (B+C)+ (C+A) aligned & z ₁+ z ₂+ z ₃=( A-i A) & +( B-i B)+( C-i C) & =( A+ B+ C)-i( A+ B+ C)=0 & 1 z₁ + 1 z₂ + 1 z₃ =0 [ z = 1 z ] & z₁ z₂+z₂ z₃+z₃ z₁=0 & ( A+i A)( B+i B)=0 & ( A B- A B) & +i( A B+ A B)=0 & (A+B)+i (A+B)=0 & (A+B)=0 ali