WBJEE2014MathematicsComplex NumberActual
In the argand plane, the distinct roots of 1+z+z³+z⁴=0(z is a complex number) represent vertices of
Options
- Aa square
- Ban equilateral triangle
- Ca thombus
- Da rectangle
Correct answer
B. an equilateral triangle
Step-by-step solution
Given equation is 1+z+z³+z⁴=0 (1+z)+z³(1+z)=0 (1+z) (1+z³ )=1 z=-1, z³=-1 z=-1, z=-1,- - ² Hence, these roots are the vertices of an equilateral triangle.