Complex Numbers questions
967 published questions with worked solutions.
- Let z ∈ C be such that |z| < 1. If = 5 + 3z 5(1 - z) , then:
- If a > 0 and z = (1 + i)^2 a - i , has magnitude 25 , then z is equal to:
- Let z_0 be a root of the quadratic equation, x^2 + x + 1 = 0. If z = 3 + 6iz_0^ 81 - 3iz_0^ 93 , then arg z is equal to:
- Let α and β be two roots of the equation x^2 + 2x + 2 = 0, then ^ 15 + ^ 15 is equal to:
- Let A = (- 2, ) : 3 + 2i 1 - 2i is purely imaginary . Then the sum of the elements in A is:
- The equation |z − i| = |z − 1|, i = -1 , represents:
- Let z_1 and z_2 be two complex numbers satisfying |z_1| = 9 and |z_2 - 3 - 4i| = 4. Then the minimum value of |z_1 - z_2| is:
- If z - z + (α ∈ R) is a purely imaginary number and |z| = 2, then a value of α is:
- Let z be a complex number such that |z| + z = 3 + i (where i = -1 ). Then |z| is equal to:
- Let (-2 - 13i )^3 = x + iy 27 (i = -1 ), where x and y are real numbers, then y − x equals:
- Let z = ( 3 2 + i2 )^5 + ( 3 2 - i2 )^5. If R(z) and I(z) respectively denote the real and imaginary parts of z, then:
- Let z ∈ C with Im(z) = 10 and it satisfies 2z - n 2z + n = 2i - 1 for some natural number n. Then:
- If 3+i 4-i , [0,2 ], is a real number, then an argument of +i is:
- If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be -
- Let z be a complex number such that | z-i z+2i |=1 and |z|= 5 2 . Then the value of |z+3i| is :
- If z_1, z_2 are complex numbers such that Re (z_1)=|z_1-1|, Re (z_2)=|z_2-1| and (z_1-z_2)= 6 , then Im (z_1+z_2) is equal to -
- Let S = z ∈ C : |z − 1| = 1 and ( 2 - 1)(z + z) - i(z - z) = 2 2 . Let z_1, z_2 ∈ S be such that |z_1| = _ z S |z| and |z_2| = _...
- Let P = z ∈ C: |z + 2 − 3i| ≤ 1 and Q = z ∈ C: z(1 + i) + z(1 − i) ≤ −8 . Let in P ∩ Q, |z − 3 + 2i| be maximum and minimum at...
- The area (in sq. units) of the region S = z ∈ C; |z − 1| ≤ 2; (z + z) + i(z − z) ≤ 2, Im(z) ≥ 0 is
- Let α and β be the sum and the product of all the non-zero solutions of the equation ( z)^2 + |z| = 0, z ∈ C. Then 4(α² + β²) is...
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