Mathematics questions
18011 published questions with worked solutions.
- If + + = + + =0, then 3 + 3 + 3 equals
- The equation z z+(2-3i)z+(2+3i) z+4=0 represents a circle of radius
- If the real part of z+2 z-1 is 4, then the locus of the point representing z in the complex plane is
- Statement 1: If |z_1|=1, |z_2|=2, |z_3|=3 and |z_1+2z_2+3z_3|=6, then value of |z_2z_3+8z_3z_1+27z_1z_2| is 36 Statement 2:...
- The complex numbers z_1,z_2,z_3 are the vertices of a triangle. Then the complex number z which makes the triangle into a...
- The trigonometric form of z=(1-i 8)^3 (where i= -1 ) is
- If z be the conjugate of the complex number z, then which of the following relations is false?
- If a= 4 3+i 4 3, then the value of ( 1+a 2 )^ 3n is
- The equation of a circle whose radius and centre are r and z_0 respectively, is
- 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