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.

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