JEE Advanced Level Test: Complex Number- 1 - EmSAT Achieve MCQ

If z is a complex number, then represents

If x_n = then x₁, x₂, x₃, .....∞

If w is a complex cube root of unity then the value of (1 + ω) (1 + ω​)² (1 + ω⁴​) (1 + ω⁸​)...2n terms =

If x² + x + 1 = 0, then the value of   is

f |z - 2 + 2i| = 1, then the least value of |z| is

If |z + 2 - i| = 5 and the maximum value of |3z + 9- 7i| is M, then the value of M is ______.

The value of  log   is

If  is purely imaginary then the locus of z is

If z_r = where r = 1,2,3,4,5 then z₁z₂z₃z₄z₅ =

For all complex numbers z₁z₂ such that |z₁| = 12 and |z₂ - 3 - 4i| = 5 the  minimum value of |z₁ -z₂| is

If a and b are real numbers between 0 and 1 such that the points z₁ = a + i, z₂ = 1 + bi and z₃ =0 form an equilateral triangle then a, b are

If α,β are the roots of x² - 2x + 4 = 0 then αⁿ + βⁿ =

The value of   is

If the cube roots of unity are 1, ω,ω² , then the roots of the equation ( x - 1)³ + 8 = 0 are

If |z₁| = 2, |z₂| = 3, |z₃| = 4 and |z₁ + z₂ + z₃| = 5 then |4z₂z₃ + 9z₃z₁ + 16z₁z₂| =

Let z = x + iy be a complex number where x and y are integers then the area of the rectangle whose vertices are the roots of the equation 

If a + ib = , then (a, b) equals

If z ∈ C and 2z =| z |+i, then z equals 

Suppose,  a, b, c ∈ C , and | a |=| b |=| c |= 1 and abc  = a +b + c, then bc +ca + ab is equal to 

The number of complex numbers z which satisfy z² + 2 | z |² = 2 is

The complex numbers sin x + i cos 2x and cos x - i sin 2x are conjugate to each other for

If z₁ and z₂ are two complex numbers are a, b are two real numbers,then |az₁ - bz₂|² + |bz₁ + az₂|² equals

If z ≠ 0 is a complex number such that arg(z) = π/4,then

Let z and w be two non-zero complex numbers such that |z| = |w| and arg (z) + arg (w) = π. Then z is equal to

If z₁, z₂, z₃ are complex numbers such that

|z₁| = |z₂| = |z₃| =|1/z₁ +1/z₂ + 1/z₃| = 1, then find the value of  z₁+ z₂ + z₃ .

If (x + iy)^1/3 = a + ib, then  x/a + y/b  equals