Cube Root of a Complex Number
Trending Questions
Q. If ω is a cube root of unity, then (1+ω)3−(1+ω2)3=
0
ω
- ω2
- None of these
Q. If ω is a cube root of unity, then (1+ω−ω2)(1−ω+ω2) =
[MNR 1990; MP PET 1993, 2002]
[MNR 1990; MP PET 1993, 2002]
1
0
- 2
- 4
Q. If α and β are imaginary cube roots of unity, then α4+β4+1αβ
[IIT 1977]
[IIT 1977]
- 0
3
- 1
- 2
Q.
Sum of the common roots of z2006+z100+1=0
and z3+2z2+2z+1=0 is
0
-1
1
2
Q. Let 1, ω and ω2 be the cube roots of unity. The least possible degree of a polynomial with real coefficients, having 2ω2, 3+4ω, 3+4ω2 and 5−ω−ω2 as roots is
Q. The polynomial x6+4x5+3x4+2x3+x+1 is divisible by (where ω is one of the imaginary cube roots of unity)
- x+ω
- x+ω2
- (x+ω)(x+ω2)
- (x−ω)(x−ω2)
Q. Let ω is the root of the equation x2+x+1=0 whose imiginary part is postive and |z−ω|=|z+ω|, then arg(z) is
- π3
- 5π6
- π6
- π4
Q. Let z0 be a root of the quadratic equation, x2+x+1=0. If z=3+6iz810−3iz930, then argz is equal to :
- π4
- π6
- π3
- 0
Q. Let ω≠1 be a cube root of unity. Then the minimum of the set
{|a+bω+cω2|2:a, b, c distinct non-zero integers} equals
{|a+bω+cω2|2:a, b, c distinct non-zero integers} equals
Q. Let α and β be roots of the equation x2−x+1=0. Then the value of α+β+α2+β2+⋯+α100+β100 is
- −3
- −1
- 0
- 3