Complex Numbers questions
967 published questions with worked solutions.
- Which one of the following is a square root of 2a+2 a^2+b^2 , where a, b R and i= -1 ?
- Consider the following statements in respect of the roots of the equation x^3-8=0 : 1. The roots are non-collinear. 2. The roots...
- If i= -1 , then how many values does i^ -2n have for different n Z ?
- Let S be the set of all complex numbers z satisfying |z^2 + z + 1| = 1. Then which of the following statements is/are TRUE?
- For a complex number z, let Re (z) denote the real part of z. Let S be the set of all complex numbers z satisfying z^4 - |z|^4 =...
- Let _1, _2, , _ 10 be positive valued angles (in radian) such that _1 + _2 + + _ 10 = 2 . Define the complex numbers z_1 = e^ i...
- For any complex number w = c + id, let (w) (- , ], where i = -1 . Let and be real numbers such that for all complex numbers z = x...
- Let z be a complex number with non-zero imaginary part. If 2 + 3z + 4z^2 2 - 3z + 4z^2 is a real number, then the value of |z|^2...
- Let z denote the complex conjugate of a complex number z and let i = -1 . In the set of complex numbers, the number of distinct...
- Let z denote the complex conjugate of a complex number z. If z is a non-zero complex number for which both real and imaginary...
- Let z be a complex number satisfying |z|^3 + 2z^2 + 4 z - 8 = 0, where z denotes the complex conjugate of z. Let the imaginary...
- Let the minimum value v_ 0 of v = |z|^ 2 + |z − 3|^ 2 + |z − 6i|^ 2 , z C is attained at z = z_ 0 . Then |2z_ 0 ^ 2 - z̄_ 0 ^ 3 +...
- Let S = z C : z^ 2 + z̄ = 0 . Then _ z S (Re(z) + Im(z)) is equal to _____ .
- The number of points of intersection of |z − (4 + 3i)| = 2 and |z| + |z − 4| = 6, z C, is
- Let for some real numbers and , a = - i . If the system of equations 4ix + (1 + i)y = 0 and 8( (2 /3) + i (2 /3))x + āy = 0 has...
- The area of the polygon, whose vertices are the non-real roots of the equation z̄ = iz^ 2 is :
- Let z = a + ib, b 0 be complex numbers satisfying z^ 2 = z̄·2^ 1−|z| . Then the least value of n N, such that z^ n = (z + 1)^ n ,...
- Let S_ 1 = z_ 1 C : |z_ 1 − 3| = 1/2 and S_ 2 = z_ 2 C : |z_ 2 - |z_ 2 + 1|| = |z_ 2 + |z_ 2 − 1|| . Then, for z_ 1 S_ 1 and z_ 2...
- Sum of squares of modulus of all the complex numbers z satisfying z̄ = iz^ 2 + z^ 2 - z is equal to _____ .
- The number of elements in the set z = a + ib C : a, b Z and 1 < |z − 3 + 2i| < 4 is _____
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