Let z₁, z₂, z₃ be the non-zero complex roots of the equation z^2 + (1+i) z = 0 . The area of the triangle formed by z₁, z₂, z₃ in the Argand plane is :

Step-by-step solution

Given equation: z^2 + (1+i) z = 0 Taking the modulus of both sides: |z^2| = |-(1+i) z | |z|^2 = 1^2 + 1^2 | z | |z|^2 = 2 |z| Since z is a non-zero complex number, we can divide by |z| : |z| = 2 Now, multiply the original equation by z : z^3 + (1+i)z z = 0 z^3 + (1+i)|z|^2 = 0 Substitute |z|^2 = 2 : z^3 + 2(1+i) = 0 z^3 = -2(1+i) The roots z₁, z₂, z₃ are the cube roots of -2(1+i) . In the Argand plane, the n -th roots of a complex number form a regular n -gon inscribed in a circle of radius R = |W|^ 1/n . Here, the