Complex Numbers...

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

The inequality  | z  − 4 | < | z  −2 | represents the region given by

If (√3 + i)¹⁰ = a + ib: a, b  ∈ R, then a and b are respectively :

Let  x,y ∈R, hen x + iy is a non real complex number if

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

Multiplicative inverse of the non zero complex number x + iy (x,y ∈R,)

The locus of z which satisfied the inequality log_0.3 |z –1| >log_0.3 |z –i| is given by

The inequality  | z  − 6 | < | z  − 2 | represents the region given by

Distance of the representative of the number 1 + I from the origin (in Argand ’s diagram) is

If  ω is a cube root of unity , then  (1+ω)(1+ω² )(1+ω⁴ )(1+ω⁸ )...... upto 2n factors is

If points corresponding to the complex numbers z₁ , z₂ , z₃  and z₄  are the vertices of a rhombus, taken in order, then for a non-zero real number k

If k , l, m , n are four consecutive integers, then  is equal to :

i² +i⁴ +i⁶ +........... up to 2k + 1 terms, for all k belongs to natural numbers N.

If  i² =−1, then sum  i+i² +i³ +....... to  1000  terms is equal to

If |z₁ | = 4, |z₂ | = 4, then |z₁  + z₂  + 3 + 4i| is less than

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

If | z | = 1, then   z  ≠-1 is

In z = a + b ι, if i is replaced by −ι, then another complex number obtained is said to b

If  = 2ⁿ  α, then  αis equal to :

If (x + iy) (3 - 4i) = (5 + 12i), then  

The locus of the equation