Let the two values of z= 1-i 1+i be z₁ and z₂ . If - 2 < Arg ( z ₁ ) < Arg ( z ₂ ) < , then ( z ₁ )+ ( z ₂ )=

Step-by-step solution

Given z= (1-i) (1+i) = (1-i) (1+i) (1-i) (1-i) z= (1-i)^2 1+1 = (1-i)^2 2 z= (1-i) 2 So,we have z₁= 1-i 2 and z₂= -(1-i) 2 = -1+i 2 (z₁ )= ( 1-i 2 )= ( 1 2 - i 2 ) (z₁ )=- ⁻¹ ( ( 1 2 ) ( 1 2 ) )=- 4 ...(i) And (z₂ )= ( -1+i 2 )= (- 1 2 +i 1 2 ) (z₂ )= + ⁻¹ ( - 1 2 1 2 )= - 4 (z₂ )= 3 4 ...(ii) From (i) and (ii) (z₁ )+ (z₂ )=- 4 + 3 4 = 2 4 = 2