Mathematics questions
18011 published questions with worked solutions.
- If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i where i= -1 , then (a+b) equal to
- If complex number z(z 2) satisfies the equation z^2=4z+|z|^2+ 16 |z|^3 then the value of |z|^4 is
- Let z=9+bi where b is non zero real and i^2=-1. If the imaginary part of z^2 and z^3 are equal, then b/3 is
- If z be a complex number satisfying z^4+z^3+2z^2+z+1=0, then |z| is equal to
- Modulus of non zero complex number z, satisfying z+z=0 and |z|^2-4zi=z^2 is
- Let A= a R the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+2a^2=0 has at least one real root . Then the value of a^2 2 is
- The minimum value of the expression E=|z|^2+|z-3|^2+|z-6i|^2 is m then the value of m/5 is
- If the complex numbers x and y satisfy x^3-y^3=98i and x-y=7i then x=a+ib where a,b R. The value of (a+b)/3 equals
- Suppose that z is a complex number that satisfies |z-2-2i| 1. The maximum value of |2iz+4| is equal to
- Let Z_1=(8+i) +(7+4i) and Z_2=(1+8i) +(4+7i) are two complex numbers. If Z_1 Z_2=a+ib where a,b R. If M is the greatest value of...
- Let 1,w,w^2 be the cube root of unity. The least possible degree of a polynomial with real coefficients having roots 2w,(2+3w),...
- If is the imaginary cube root of unity, then find the number of pairs of integers (a,b) such that |a +b|=1
- If [ 1+ +i +i(1+ ) ]^4= n +i n , then n is
- If |z+2-i|=5 and maximum value of |3z+9-7i| is M then the value of M/4 is
- If x= - ^2-2, then the value of x^4+3x^3+2x^2-11x-6 is (where is cube root of unity)
- The complex number z satisfies z+|z|=2+8i. The value of (|z|-8) is
- Number of positive integers x for which f(x)=x^3-8x^2+20x-13 is a prime number is
- Let and be the solutions of the quadratic equation x^2-1154x+1=0, then the value of [4] + [4] is equal to
- f:R R, f(x)= 3x^2+mx+n x^2+1 . If the range of this function is [-4,3], then find the value of |m+n| is
- Suppose a,b,c I such that greatest common divisor of x^2+ax+b and x^2+bx+c is (x+1) and the least common multiple of x^2+ax+b and...