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 | z2 - 1 | = | z |2 + 1 , then z lies on
A circle
An ellipse
Real axis
Imaginary axis
Find the value of x and y if (x + iy) + (3 - 2i) = 1 + 4i
x = 6, y = -2
x = -2, y = 6
x = 3, y = -2
x = -2, y = 3
Let ∝ and β be the roots of the quadratic equation x2 + px + p3 = 0 (p ≠ 0). If (∝,β) is a point on the parabola y2 = x, then roots of the quadratic equation are
4 and -2
-4 and -2
4 and 2
-4 and 2
PQ and PR are two infinite rays,QAR is an arc.The point lying in the shaded region excluding the boundary , satisfies.
|z - 1 | > 2 : |arg(z - 1) | < π/4
|z - 1 | > 2 : |arg(z - 1 ) | < π/2
|z - 1 | > 2 : |arg(z + 1) |
|z - 1 | > 2: |arg(z + 1) | < π/2
Both roots of equation(x - b) (x - c) + (x - a)(x - c) + (x - a)(x -b) = 0 are always
Positive
Negative
Real
None of these
The polar form of complex number -4 + i4 √3
2 [cos (π/3) + i sin (π/3) ]
4 [cos (2π/3) + i sin (2π/3 ) ]
8 [ cos (2π/3 ) + i sin (2π/3 ) ]
12 [ cos (3π/4) + i sin (3π/4 ) ]
If roots of equation x2 - 5x + 16 = 0 are ∝,β and roots of equation x2 + px + q = 0 are ∝2 + β2 and ∝β/2 then
p = 1 and q = -56
p = -1 and q = -56
p= 1 and q = 52
p = -1 and q = 56
The positive value of 'a' for which equations x2 + ax + 64 = 0 and x2 - 8x + a = 0 will both have real roots is
a = 20
a = 16
a = 8
a = 4
The polar form of complex number sin 120o - i cos 120o is