Complex Numbers questions
967 published questions with worked solutions.
- Let z, w be complex numbers such that z + i w = 0 and zw = . Then z equals
- If z = x - iy and z^ 1 3 = p + iq, then ( x p + y q ) (p^2 + q^2) is equal to
- If |z^2 - 1 | = |z|^2 + 1, then z lies on
- If the cube roots of unity are 1, , ^2 then the roots of the equation (x - 1)^3 + 8 = 0, are
- If z_1 and z_2 are two non-zero complex numbers such that |z_1 + z_2| = |z_1| + |z_2| then z_1 - z_2 is equal to
- If = z z - 13i and | | = 1, then z lies on
- If z^2 + z + 1 = 0, where z is a complex number, then the value of (z + 1z )^2 + (z^2 + 1 z^2 )^2 + (z^3 + 1 z^3 )^2 + + (z^6 + 1...
- The value of _ k=1 ^ 10 ( 2k 11 + i 2k 11 ) is
- The conjugate of a complex number is 1 i - 1 . Then the complex number is
- If |z - 4z | = 2, then the maximum value of |z| is equal to
- If α and β are the roots of the equation x^2 - x + 1 = 0, then ^ 2009 + ^ 2009 =
- The number of complex numbers z such that |z - 1| = |z + 1| = |z - i| equals
- If ( 1) is a cube root of unity, and (1 + )^7 = A + B . Then (A, B) equals
- If P(x,y) denotes z=x+iy, x,y IR and i= -1 in Argand's plane and | z-1 z+2i |=1, then the locus of P is
- If a>0 and z= (1+i)^2 a-i , i= -1 has magnitude 2 5 , then z is equal to
- If z^2 + z + 1 = 0 then (z^3 + 1 z^3 )^2 + (z^4 + 1 z^4 )^2 = where z = w = complex cube root of unity
- If |z|=1 and w= z-1 z+1 (where z -1) then Re (w) is
- If | z 1 + i | = 2, where z = x + iy, i = -1 represents a circle, then centre 'C' and radius 'r' of the circle are
- If and are imaginary cube roots of unity, then value of ^4+ ^ 28 + 1 is
- The Cartesian form of complex number z=4( 300^0+i 300^0), where i= -1 is
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