a = 0 and b = 1
a = 1 and b = 0
a = 2 and b = -1
a = -1 and b = 2
If P is a multiple of n , then the sum of Pth power of nth roots of unity is
p
n
0
None of these
If the complex numbers z1,z2 and z3 represent the vertices of an equilateral triangle such that | z1 | = | z2 | = | z3 | , then the sum of z1,z2 and z3 is
-1
1
2
If |z - 3 + i | = 4, then the locus of z = x + iy is
x2 + y2 = 0
x2 + y2 - 6 = 0
x2 + y2 - 3x + y - 6 = 0
x2 + y2 - 6 x + 2 y - 6 = 0
The polar form of complex number 1 + i is
√2 (cos π/4 + i sin π/4 )
√2 (cos 2π/4 + i sin 2π/4
√2 (cos π/4 - i sin π/4 )
√3 (sin 2π/4 + i cos 2π/4)
If we express in the form of x + iy, we get
cos 49θ - i sin 49θ
cos 23θ + i sin 23θ
cos 49θ + i sin 49θ
cos 21θ + i sin 21θ
(x = 3, y = 1 )
(x = 1, y = 3 )
(x = 0 , y = 0 )
If 1, a1 , a2 , a3 . . . an-1 are the nth roots of unity , then the value of (1 - a1) (1 - a2) (1 - a3) . . . (1 - an-1) is
- n
The complex numbers z1,z2 and z3 satisfying are the vertices of a triangle, which is
Of zero area
Equilateral
Right - angled isosceles
Obtuse - angled isosceles
