Mathematics questions
18011 published questions with worked solutions.
- Let z_1,z_2,z_3 be the roots of the equation x^3+bx^2+cx+d=0, b,c,d R. If z_1=1, z_2=1+Ai (A 0, A R), then evaluate d+c-b.
- A complex number z satisfies ( z z-i )= 3 and |z|=|z-i|, then evaluate [ Re (2z-i) ] where [ ,] represents the greatest integer...
- If is a complex cube root of unity, then evaluate | + ^ ( 15+ 9 50 + 81 500 + 729 5000 + ) |.
- If z=x+iy and x^2+y^2=36 and the range of |x|-|y| is [a,b], then evaluate b^2-a^2.
- Two points A and B in Argand plane represent z and z_1=2 (z+ 3+i ) respectively. If A moves on a circle with centre at origin and...
- Side AB of a square joins z_1=-1 and z_2=3i, and the vertices C(z_3) and z_4 lie in the second quadrant of Argand plane. Evaluate...
- If and are roots of x^2-4x+8=0 and ^ 24 + ^ 24 =2^k( p +i p ), then evaluate k+p.
- If z is a complex number such that |z| 3, then find the minimum value of |z+ 34 |.
- If Re [(1+i)^ -i ]=e^ p (m n), then evaluate pmn.
- If z and w are non-zero complex numbers such that |zw|=1, (z)- (w)= 2 and zw=a+ib, then find a^2+b^2.
- If and are the roots of the equation ix^2-x+12i=0, then find + .
- The complex equation of straight line L is (4+3i)z+(4-3i) z=24. Find the area of the triangle formed by L, real and the imaginary...
- If |z-25i| 15 and | . (z)- . (z)| is m ^ -1 pq, then find mp-q. (Given that G.C.D. (p,q)=1)
- If is a complex cube root of unity, then find the value of ( a+b +c ^2 c+a +b ^2 + a+b +c ^2 b+c +a ^2 )^2.
- If _ 3 |z|^2-|z|+1 2+|z| 2, then find the least value of |z|.
- Find the least value of k for which |z-2 3i|=k intersects the curve z= 6.
- If |z+4|^2-|z-4|^2=8, then find Re (z).
- Find the sum of all possible values of Im (z) where | z-12 z-8i |= 53 and | z-4 z-8 |=1.
- Find the digital sum of the value of 1(2- ) (2- ^2 )+2(3- ) (3- ^2 )+ +9(10- ) (10- ^2 ), where is a complex cube root of unity.
- If 2 2z=( 3-1)+i( 3+1), then find Re (z^6 ).