In the argand plane, the distinct roots of 1+ z+ z^3 + z^4 = 0 (z is a complex number) represent vertices of (1) a square (2) an equilateral triangle (3) a rhombus (4) a rectangle

Solution:

1+ z+ z³ + z⁴ = 0

=> (1+z)+z³(1+z) = 0

=> (1+z³)(1+z) = 0

z = -1

z³ = -1

z = -1, – ω, -ω² are cube roots of unity

So these are the vertices of an equilateral triangle.

Hence option (3) is the answer.