Complex Numbers questions
967 published questions with worked solutions.
- If z 0 be a complex number such that |z − 1/z| = 2, then the maximum value of |z| is:
- Let S = z = x + iy : |z − 1 + i| |z|, |z| < 2, |z + i| = |z − 1| . Then the set of all values of x, for which w = 2x + iy S for...
- If z = 2 + 3i, then z^ 5 + (z̄)^ 5 is equal to :
- Let be a root of the equation 1 + x^ 2 + x^ 4 = 0. Then the value of ^ 1011 + ^ 2022 - ^ 3033 is equal to
- Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and (z - 1) - (z + 1) = /4 intersect
- Let and be the roots of the equation x^ 2 + (2i - 1) = 0. Then, the value of | ^ 8 + ^ 8 | is equal to:
- Let S = z C : |z − 2| 1, z(1 + i) + z̄(1 − i) 2 . Let |z − 4i| attains minimum and maximum values, respectively, at z_ 1 S and z_...
- If A= x Z : x^3-1=0 and B= x Z : x^2+x+1=0 , where Z is set of complex numbers, then what is A B equal to?
- The common roots of the equations z^3+2z^2+2z+1=0 and z^ 2017 +z^ 2018 +1=0 are
- For a non-zero complex number z, let arg(z) denote the principal argument of z, with −π < arg(z) ≤ π. Let ω be the cube root of...
- Let A = (0,3 ): 1+2i 1-i is purely imaginary . Then the sum of the elements of A is
- If for z = +i , |z + 2| = z + 4(1 + i), then + and are the roots of the equation
- Let S = z=x+iy: 2z-3i 4z+2i is a real number . Then which of the following is NOT correct?
- Let the complex number z = x + iy be such that 2z-3i 2z+i is purely imaginary. If x+y^2=0, then y^4+y^2-y is equal to
- For a C, let A = z C : Re(a + z) > Im( a + z) and B = z C : Re(a + z) < Im( a + z) . Then among the two statements : (S1) : If...
- Let S = z C- i,2i : z^2+8iz-15 z^2-3iz-2 R . If - 13 11 i S, R- 0 , then 242 ^2 is equal to
- Let w_1 be the point obtained by the rotation of z_1 = 5 + 4i about the origin through a right angle in the anticlockwise...
- Let C be the circle in the complex plane with centre z_0= 1 2 (1+3i) and radius r =1. Let z_1=1+i and the complex number z_2 be...
- Let S = z C: z=i(z^2+Re( z)) . Then _ z S |z|^2 is equal to :
- If the set Re ( z- z+z z 2-3z+5 z ):z C,Rez=3 is equal to the interval ( , ], then 24( - ) is equal to-
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