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 equations of the transverse and conjugate axes of a hyperbola respectively are x + 2 y - 3 = 0, 2 x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2 y - 3)2 - 3/5 (2 x - y + 4)2 = 1
2/5 (2 x - y + 4)2 - 3/5 (x + 2 y - 3)2 = 1
2 (2 x - y + 4 )2 - 3 (x + 2 y - 3)2 = 1
2 (x + 2 y - 3)2 - 3 (2 x - y + 4)2 = 1
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
The solution of the equation | z | - z = 1 + 2i is
2 - 3/2 i
3/2 + 2i
3/2 - 2i
-2 + 3/2 i
If and | ω | = 1, then z lies on
A circle
An ellipse
A parabola
A straight line
If the amplitude of a complex number is π/2, then the number is
Purely imaginary
Purely real
0
Neither real nor imaginary
If P is a multiple of n , then the sum of Pth power of nth roots of unity is
p
n
None of these
The value of is
1/5
-1/5
1/10
-1/10
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
a = 0 and b = 1
a = 1 and b = 0
a = 2 and b = -1
a = -1 and b = 2
