Complex Numbers questions
967 published questions with worked solutions.
- Let z_1= ( 3+i)^2 (1- 3i) 1+i , z_2= (1+ 3i)^2 ( 3-i) 1-i . Then
- If |z_1+z_2|=|z_1-z_2| then
- If |z_1+z_2|^2=|z_1|^2+|z_2|^2 then
- If -1 = i, and is a nonreal cube root of unity then the value of vmatrix 1 & ^2 & 1+i+ ^2 -i & -1 & -1-i+ 1-i & ^2-1 & -1 vmatrix...
- The values of x [-2 ,2 ] such that x+i x 1+i , i= -1 , is purely imaginary, are given by
- The equation x^3+y^3=0 represents
- f : R R R such that f(x + iy) = + x^2 + y^2 . Then f is
- Two vertices of an equilateral triangle in the Argand plane represent the nonreal cube roots of unity. The area of the triangle is
- If |z - 2 z | = 1 then the greatest value of |z| is
- If |z_1 - z_0| = |z_2 - z_0| = a and amp z_2 - z_0 z_0 - z_1 = 2 then z_0 is equal to
- The minimum value of |z - 1| + |z| for complex values of z is
- If is a nonreal root of x^5 + 1 = 0 then ^ 10n+2 + ^ 5n+2 + ^ 5n , where n is an odd positive integer, has the value
- If z = 1 + 2 3 + i 2 3 then
- The number of elements in the set S= i^n+i^ -n : n is an integer where i= -1 , is
- The origin, z_1 and z_2 are the vertices of an equilateral triangle where z_1,z_2 are roots of the equation z^2+az+b=0. Then
- If z_1 and z_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2| then z_1- z_2 is equal to
- If z_1, z_2 be two nth roots of unity such that they represent two points A, B in the Argand plane where AOB=60^ and O is the...
- Which of the following is equal to [3] -1 ?
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- z is a unimodular complex number. STATEMENT-1: (z^2 + z) = z. STATEMENT-2: z = ( z) - i ( z)
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