Paragraph: Let Z₁ and Z₂ be any two complex numbers such that Z₁^2+Z₂^2+Z₁ Z₂=0 Question: What is the value of 1 2 + Re ( Z ₁ Z ₂ ) ?

Step-by-step solution

Given that, Z₁^2+Z₂^2+Z₁ Z₂=0 Z₁=w and Z₂=w^2 Now, aligned & 1 2 + Re ( Z₁ Z₂ )= 1 2 + Re ( ^2 )= 1 2 + Re ( ^2 ) & = 1 2 + Re (- 1 2 - 3 2 i )= 1 2 + (- 1 2 )=0 & =0 aligned