Complex Numbers...

If (-1 + √ 3i)ⁿ + (-1 - √ 3i)ⁿ = 2ⁿ , then  is equal to

The complex numbers z = x + y i which satisfy the equation  = 1 lie on

If k, l, m, n are four consecutive integers, then jk + jl + jm + jn is equal to

If x = , then x³ equals

Find the value of (1 + )⁴.

If │z│= 1, then z - 1/(z + 1), z ≠ -1 is

If w  is cube root of unity, then ( 1 + w) ( 1 + w²) ( 1 + w⁴) ( 1 + w⁸)… upto 2n factors is

If w is a non real cube root of unity and (1+ w)⁹ = a + b w; a, b  R, then a and b are respectively the numbers

Let x, y R, then x + yi is a non- real complex number if

The inequality │z - 4│< │z - 2│represents the region given by

z + z` ≠  0 if and only if

Multiplicative inverse of the non- zero complex number x + yi (x, y R) is

Locus of z = 2 + i Im (z) is given by

i² + i⁴ + i⁶ +…. Upto 2 k + 1  terms, k ª N, is

If (x + yi) (3 - 4i) = 5 + 12i, then √ (X² + y² ) =

2 √ -9 √ -16, is equals to

Let x, y R, then x + yi is a purely imaginary number if

The inequality │z - 6│< │z - 2│represents the region given by

If (√ 3 + i )¹⁰ = a + bi ; a, b ª  R, then a and b are respectively

The equation │4z - 1│ = 4 │z - 5│ represents