If the cube roots of unity are 1, ω, ω^{2}, then the roots of the equation (x – 1)^{3} + 8 = 0 are (1979)
The smallest positive integer n for which (1980)
= 1 is
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The complex numbers z = x+ iy which satisfy the equation lie on....... (1981  2 Marks)
The inequality z – 4 < z –2 represents the region given by (1982  2 Marks)
If z = x + iy and ω = (1  iz) /( z  i) , then ω= 1 implies that, in the complex plane, (1983  1 Mark)
The points z_{1}, z_{2}, z_{3} z_{4} in the complex plane are the vertices of a parallelogram taken in order if and only if (1983  1 Mark)
If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 – r) a + rb and w = (1 – r)u + rv, where r is a complex number, then the two trian gles (1985  2 Marks)
If ω (≠1) is a cube root of unity and (1 + ω)^{7} = A + B ω then A and B are respectively (1995S)
Let z and ω be two non zero complex numbers such that z = ω and Arg z+ Arggω = π, then z equals (1995S)
Let z and ω be two complex numbers such that z ≤1, ω ≤ 1 and z + iω =  z – i  = 2 then z equals (1995S)
For positive integers n_{1}, n_{2} the value of the expression (1 + i)^{n1} + (1 + i^{3})^{n1} + (1+ i^{5})^{n2} + (1+i^{7})^{n2} , where i = – is a real number if and only if (1996  1 Marks)
If i = , then 4 + 5 + 3 is equal to (1999  2 Marks)
If arg(z) < 0, then arg (z)  arg(z) = (2000S)
If z_{1}, z_{2} and z_{3} are complex numbers such that (2000S)
z_{1} = z_{2} = z_{3} = = 1, then z_{1} +z_{2} +z_{3} is
Let z_{1 }an d z_{2} be n^{th }roots of unity which subtend a right angle at the origin . Then n must be of the form (2001S)
The complex numbers z_{1}, z_{2} and z_{3} satisfying are the vertices of a triangle which is
For all complex numbers z_{1}, z_{2} satisfying z_{1}=12 and  z_{2}34i = 5, the minimum value of z_{1}z_{2} is (2002S)
If z = 1 and ω = ( where Z ≠ 1) , then Re(ω) is
If ω(≠1) be a cube root of unity and (1 + ω^{2})^{n} = (1 + ω^{4})^{n}, then the least positive value of n is (2004S)
The locus of z which lies in shaded region (excluding the boundaries) is best represented by (2005S)
a, b, c are integers, not all simultaneously equal and ω is cube root of unity (ω ≠ 1), then minimum value of a + bω + cω^{2} is (2005S)
Let ω = +i then the value of the det.
(2002  2 Marks)
If is purely real where w = α + iβ, β ≠ 0 and z ≠ 1,then the set of the values of z is (2006  3M, –1)
A man walks a distance of 3 units from the origin towards the northeast (N 45° E) direction. From there, he walks a distance of 4 units towards the northwest (N 45° W) direction to reach a point P. Then the position of P in the Argand plane is (2007 3 marks)
If z = 1 and z ≠ ± 1, then all the values of lie on (2007 3 marks)
A particle P starts from the point z_{0} = 1 + 2i, where i = .It moves horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1.From z1 the particle moves units in the direction of the vector and then it moves through an angle in anticlockwise direction on a circle with centre at origin, to reach a point z_{2}. The point z_{2} is given by (2008)
Let z = cosθ + i sinθ. Then the value of
at θ = 2° is (2009)
Let z = x + iy be a complex number where x and y are integers.Then the area of the rectangle whose vertices are the roots of the equation : (2009)
Let z be a complex number such that the imaginary part of z is nonzero and a = z^{2} + z + 1 is real. Then a cannot take the value
(2012)
447 docs930 tests

447 docs930 tests
