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 , then the value of x is
cos θ ± i sin θ
cos 2θ + i sin 2θ
(cos θ + i sin θ )2
cos 4θ - i sin 4θ
If -i + 3 is a root of x2 - 6x + k = 0 then the value of k is
5
√5
√10
10
a = 0 and b = 1
a = 1 and b = 0
a = 2 and b = -1
a = -1 and b = 2
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
n
0
None of these
If conjugate and reciprocal of a complex number z = x + iy are equal , then
x + y = 1
x2 + y2 = 1
x = 1 and y = 0
x = 0 and y = 1
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)
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
The solution of the equation | z | - z = 1 + 2i is
2 - 3/2 i
3/2 + 2i
3/2 - 2i
-2 + 3/2 i
