Complex Numbers questions
967 published questions with worked solutions.
- The complex numbers x + i 2x and x - i 2x (i = -1 ) are conjugate to each other for,
- z= 3+2i 1-2i ,(i= -1 ), will be purely imaginary if =
- If z=x+iy is a complex number, then the equation | z+i z-i |= 3 represents the
- Argument of the complex number z= 13-5i 4-9i , i= -1 is
- The modulus of the square root of the complex number 6 + 8i (where i = -1 ) is
- The area of the triangle whose vertices are i, and ^2 is (Where is a complex cube root of unity other than 1, i is an imaginary...
- Let Z_1 and Z_2 be any two complex number. Statement 1: |Z_1 - Z_2| |Z_1| - |Z_2| Statement 2: |Z_1 + Z_2| |Z_1| + |Z_2|
- Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z. Statement 1: If arg Z + arg W...
- If z 1 and z^2 z - 1 is real, then the point represented by the complex number z lies
- If Z_1 0 and Z_2 be two complex numbers such that Z_2 Z_1 is a purely imaginary number, then | 2Z_1 + 3Z_2 2Z_1 - 3Z_2 | is equal...
- If a complex number z satisfies the equation z + 2|z + 1| + i = 0, then |z| is equal to :
- Let a = Im ( 1 + z^2 2iz ), where z is any non-zero complex number. The set A = a : |z| = 1 and z 1 is equal to:
- Let z satisfy |z| = 1 and z = 1 - z. Statement 1 : z is a real number. Statement 2 : Principal argument of z is 3 .
- If z_1, z_2 and z_3, z_4 are 2 pairs of complex conjugate numbers, then ( z_1 z_4 ) + ( z_2 z_3 ) equals:
- Let z -i be any complex number such that z-i z+i is a purely imaginary number. Then z + 1z is:
- For all complex numbers z of the form 1 + i , R, if z^2 = x + iy, then
- Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I (P) If α and β are the distinct...
- If z_0= +i , i= -1 , then the roots of the cubic equation x^3-2(1+ )x^2+(4 + ^2+ ^2)x-2( ^2+ ^2)=0 are
- The common roots of the equations x^3+2x^2+2x+1=0 and 1+x^ 130 +x^ 1988 =0 are (where is a nonreal cube root of unity)
- A quadratic equation whose roots are ( )^2 and ( )^2, where , , are the roots of x^3+27=0, is
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