If -i + 3 is a root of x2 - 6x + k = 0 then the value of k is
5
√5
√10
10
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
0
1
n
-n
If and | ω | = 1, then z lies on
A circle
An ellipse
A parabola
A straight line
If P is a multiple of n , then the sum of Pth power of nth roots of unity is
P
None of these
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 z1,z2 and z3 be the vertices of an equilateral triangle occurring in anticlockwise sense, then
z1 + z2 + z32 = 0
z1z2 + z2z3 + z3z1 = 0
z1 + ω z2 + ω2 z3 = 0
z12 + z22 + z32 = 2 (z1z2 + z2z3 + z3z1)
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
If we express ( 2 + 3 i ) 2 in the form of ( x + iy ) , we get
-5 + 12 i
12 - 5 i
5 - 12 i
12 + 5 i
Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex number.Further,assume that the origin , z1 and z2 form an equilateral triangle.Then
a2 = b
a2 = 2b
a2 = 3b
a2 = 4b
a = 0 and b = 1
a = 1 and b = 0
a = 2 and b = -1
a = -1 and b = 2
