Complex Numbers questions
967 published questions with worked solutions.
- Let p, q R and (1- 3i)^ 200 =2^ 199 (p+iq), i = -1 , then p + q^2 and p – q + q^2 are roots of the equation
- Let z be a complex number such that | z-2i z+i |=2, z –i. then z lies on the circle of radius 2 and centre
- Let z be a complex number such that | z-2i z+i |=2, z –i. then z lies on the circle of radius 2 and centre
- Let z_1 = 2 + 3i and z_2 = 3 + 4i. The set S = z C : |z-z_1|^2-|z-z_2|^2=|z_1-z_2|^2 represents
- Let = 8 – 14t, A = z C: z- z z^2-( z)^2-112i and B = z C:|z+3i|=4 . Then _ z A B (Rez-Imz) is equal to _________.
- For two non-zero complex numbers z_1 and z_2, if Re(z_1z_2) = 0 and Re(z_1+z_2), then which of the following are possible ? A....
- Let z = 1 + i and z_1= 1+ z z(1-z)+ 1 z . Then 12 arg(z_1) is equal to________.
- The complex number z = i-1 3 +i 3 is equal to :
- A man walks a distance of 3 units from the origin towards the north-east (N 45° E) direction. From there, he walks a distance of...
- If |z| = 1 and z ≠ ±1, then all the values of z 1 - z^2 lie on
- A particle P starts from the point z_0 = 1 + 2i, where i = -1 . It moves first horizontally away from origin by 5 units and then...
- 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...
- Let ℝ denote the set of all real numbers. Let z_1 = 1 + 2i and z_2 = 3i be two complex numbers, where i = -1 . Let S = (x, y) R R...
- z and w are two non zero complex no.s such that |z| = |w| and Arg ,z + Arg ,w = then z equals
- If |z - 4| < |z - 2|, its solution is given by
- The locus of the centre of a circle which touches the circle |z - z_1| = a and |z - z_2| = b externally ( z, z_1 and z_2 are...
- If z and are two non-zero complex numbers such that |z | = 1 and Arg (z) - Arg ( ) = 2 , then z is equal to
- Let Z_1 and Z_2 be two roots of the equation x^2 + aZ + b = 0 being complex. Further, assume that the origin, Z_1 and Z_2 form an...
- If ( 1+i 1-i )^x = 1 then
- If 1, , ^2 are the cube roots of unity, then = vmatrix 1 & ^n & ^ 2n ^n & ^ 2n & 1 ^ 2n & 1 & ^n vmatrix is equal to
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