Practice questions
88551 published questions with worked solutions.
- The complex numbers x+i 2x and x-i 2x are conjugate to each other for
- The least positive integer n for which ( 1+i 1-i )^n is real, is
- Consider the following statements: I. The points having affixes z_1,z_2,z_3 from an equilateral triangle, iff 1 z_1-z_2 + 1...
- If ^ -1 ( +i )=x+iy, then x is equal to
- For any two complex numbers z_1 and z_2 and any real numbers a and b; |az_1-bz_2 |^2+ |bz_1+az_2 |^2 is equal to
- Let z_1 and z_2 be the non-real roots of the equation 3z^2+3z+b=0. If the origin together with the points represented by z_1 and...
- If z_1,z_2,z_3,z_4 are the affixes of four points in the argand plane and z is the affix of a point such that...
- The equation z^2= z has
- Statement 1: If z_1 and z_2 are two complex numbers such that |z_1|=|z_2|+|z_1-z_2|, then Im ( z_1 z_2 )=0 Statement 2: (z)=0 z...
- If |z-i Re (z) |= |z- Im (z) | (where i= -1 ), then z lies on
- Statement 1: If |z_1+z_2|^2=|z_1|^2+|z_2|^2, then z_1 z_2 is purely imaginary Statement 2: If z is purely imaginary, then z+ z=0
- The value of 4 ( 75^ +i 75^ ) 0.4 ( 30^ +i 30^ ) is
- If z_1,z_2,z_3,z_4 are four complex numbers represented by the vertices of a quadrilateral taken in order such that...
- If the vertices of a quadrilateral be A=1+2i, B=-3+i, C=-2-3i and D=2-2i, then the quadrilateral is
- If a= ( 2 7 )+i ( 2 7 ), then the quadratic equation whose roots are =a+a^2+a^4 and =a^3+a^5+a^6 is
- The maximum distance from the origin of coordinates to the point z satisfying the equation |z+ 1z |=a is
- The centre of a regular polygon of n sides is located at the point z=0 and one of its vertex z_1 is known. If z_2 be the vertex...
- In the argand plane, the complex number z=4-3i is turned in the clockwise sense through 180^ and stretched three times. The...
- Let _n= ( 2 n )+i ( 2 n ), i^2=-1, then (x+y _3+z _3^2 ) (x+y _3^2+z _3 ) is equal to
- If |z|= |z-2|,|z+2| , then