Complex Numbers questions
967 published questions with worked solutions.
- Let ω be a complex cube root of unity with ω ≠ 1 and P = [p_ ij ] be a n × n matrix with p_ ij = ^ i+j . Then P^2 0, when n =
- Let z_k = ( 2k 10 ) + i ( 2k 10 ); k = 1, 2, …, 9. List I P. For each z_k there exists a z_j such that z_k z_j = 1 Q. There...
- For any integer k, let _k= ( k 7 )+i ( k 7 ), where i= -1 . The value of the expression _ k=1 ^ 12 | _ k+1 - _k| _ k=1 ^ 3 | _...
- Let z= -1+ 3 i 2 , where i= -1 , and r,s 1,2,3 . Let P= bmatrix (-z)^r & z^ 2s z^ 2s & z^r bmatrix and I be the identity matrix...
- Let a, b, x and y be real numbers such that a-b=1 and y 0. If the complex number z=x+iy satisfies Im ( az+b z+1 )=y, then which...
- For a non-zero complex number z, let (z) denote the principal argument with - < (z) . Then, which of the following statement(s)...
- Let S be the set of all complex numbers z satisfying |z-2+i| 5 . If the complex number z_0 is such that 1 |z_0-1| is the maximum...
- Let 1 be a cube root of unity. Then the minimum of the set |a+b +c ^2|^2:a,b,c distinct non-zero integers equals _____
- If x + 1 x = 2 , then x^n + 1 x^n 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...
- If z = a + ib, then real and imaginary part of z are
- Two complex numbers are equal, if and only if
- If x = -16 , then
- If 4x + i(3x - y) = 3 + i(-6), where x and y are real numbers, then the values of x and y are
- a + ib > c + id can be explained only when
- If z_1 = x_1 + iy_1 and z_2 = x_2 + iy_2, then which of the following represent addition of z_1 and z_2?
- If z_1 = 2 + 3i and z_2 = 3 - 2i, then z_1 - z_2 is equal to
- If z = 5i (- 3 5 i ), then z is equal to
- If z = i^9 + i^ 19 , then z is equal to
- The value of (1 + i)^3 + (1 - i)^3 is equal to
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