Complex Numbers questions
967 published questions with worked solutions.
- Let z_ 1 and z_ 2 be two complex numbers such that z̄_ 1 = i z̄_ 2 and (z_ 1 /z̄_ 2 ) = . Then-
- Let a circle C in complex plane pass through the points z_ 1 = 3 + 4i, z_ 2 = 4 + 3i and z_ 3 = 5i. If z ( z_ 1 ) is a point on C...
- If z = x + iy satisfies |z| − 2 = 0 and |z − i| − |z + 5i| = 0, then
- Let O be the origin and A be the point z_ 1 = 1 + 2i. If B is the point z_ 2 , Re(z_ 2 ) < 0, such that OAB is a right angled...
- If z^ 2 + z + 1 = 0, z ℂ, then | _ n=1 ^ 15 (z^n + (-1)^n 1 z^n )^2 | is equal to _____.
- Let A = z C : | z+1 z-1 | < 1 and B = z C : ( z-1 z+1 ) = 2 3 . Then A B is :
- If z is a complex number such that z-i z-1 is purely imaginary, then the minimum value of |z – (3 + 3i)| is :
- Let a, b be two real numbers such that ab < 0. If the complex number 1+ai b+i is of unit modulus and a + ib lies on the circle |z...
- If the centre and radius of the circle | z-2 z-3 |=2 are respectively ( , ) and , then 3( + + ) is equal to
- Let a be two non-zero real numbers. Then the number of elements in the set X = Z C: Re(az^2+bz) = a and Re(bz^2+az) = b is
- For , , z C and >1, if -1 is the radius of the circle |z- |^2+|z- |^2=2 , then | - | is equal to __________.
- Let be a complex cube root of unity with 1. A fair die is thrown three times. If r_1, r_2 and r_3 are the numbers obtained on the...
- Let z_1 and z_2 be two distinct complex numbers and let z = (1 - t)z_1 + tz_2 for some real number t with 0 < t < 1. If Arg(w)...
- Let be the complex number 2 3 + i 2 3 . Then the number of distinct complex numbers z satisfying vmatrix z+1 & & ^2 & z+ ^2 & 1...
- If z is any complex number satisfying |z - 3 - 2i| 2, then the minimum value of |2z - 6 + 5i| is
- Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form bmatrix 1 & a & b & 1 & c ^2 & & 1...
- Let = e^ i /3 , and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x a + b + c ^2 = y a + b ^2 + c = z. Then...
- Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a **cannot** take the...
- Let complex numbers α and 1 lie on circles (x - x_0)^2 + (y - y_0)^2 = r^2 and (x - x_0)^2 + (y - y_0)^2 = 4r^2, respectively. If...
- Let w = 3 + i 2 and P = w^n : n = 1, 2, 3, . Further H_1 = z C : Re z > 1 2 and H_2 = z C : Re z < -1 2 , where C is the set of...
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