Complex Numbers questions
967 published questions with worked solutions.
- 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
- If z=x+iy, then the equation | 2z-1 z+1 |=m does not represent a circle when m=
- The equation bz+b z=c, where b is a non-zero complex constant and c is a real number, represents
- If P,P' represent the complex number z_1 and its additive inverse respectively, then the equation of the circle with PP' as a...
- If z_0= 1-i 2, then the value of the product (1+z_0) (1+z_0^2 ) (1+z_0^ 2^2 ) (1+z_0^ 2^3 ) (1+z_0^ 2^n ) must be
- If , , are the cube roots of p, p<0 then for any x,y and z the values of x +y +z x +y +z are
- Number of solutions of the equation z^2+|z|^2=0, where z C is
- Let z( 2) be a complex number such that _ 1/2 |z-2|> _ 1/2 |z|, then
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