If x_r = \(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x₁, x_2, x₃ ... x_∞ is _________

If z₁, z₂, z₃ are the vertices of a parallelogram, then the fourth vertex z₄ opposite to z₂ is _____

If x = cos θ + i sin θ, then xⁿ + \(\frac { 1 }{ { x }^{ n } } \) is ______

The value of \(\frac { (cos{ 45 }^{ 0 }+isin{ 45 }^{ 0 })^{ 2 }(cos{ 30 }^{ 0 }-isin{ 30 }^{ 0 }) }{ cos{ 30 }^{ 0 }+isin{ 30 }^{ 0 } } \) is __________

The modular of \(\frac { (-1+i)(1-i) }{ 1+i\sqrt { 3 } } \) is ______

The conjugate of \(\frac { 1+2i }{ 1-(1-i)^{ 2 } } \) is _______

If a = cos α + i sin α, b = -cos β + i sin β then \(\left( ab-\frac { 1 }{ ab } \right) \) is _________

\(\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } } \) = ________

(1+i)³ = ______

The points represented by 3 - 3i, 4 - 2i, 3 - i and 2 - 2i form _____ in the argand plane.

If ω is the cube root of unity, then the value of (1-ω) (1-ω²) (1-ω⁴) (1-ω⁸) is _________

If x = cosθ + i sinθ, then the value of xⁿ+\(\frac { 1 }{ { x }^{ n } } \) is ___________

If zⁿ = \(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z₁, z₂ ..... z₆ is _________

\(\frac { 1+e^{ -i\theta } }{ 1+{ e }^{ i\theta } } \) =__________

If z = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if _________

The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) = 1 lies on _________

The value of (1+i)⁴ + (1-i)⁴ is __________

The amplitude of \(\frac{1}{i}\) is equal to _______

If x + iy = \(\frac { 3+5i }{ 7-6i } \), they y = ___________

If z = \(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) = ___________

If z = 1-cos θ + i sin θ, then |z| = _____________

If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| = ____________

If a = 3 + i and z = 2 - 3i, then the points on the Argand diagram representing az, 3az and - az are ___________

The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\) is a positive integer is ____________

.If a = 3+i and z = 2-3i, then the points on the Argand diagram representing az, 3az and - az are _________

If a = cos θ + i sin θ, then \(\frac { 1+a }{ 1-a } \) = ___________

If z = cos\(\frac { \pi }{ 4 } \) + i sin\(\frac { \pi }{ 6 } \), then ______

If, i² = -1, then i¹ + i² + i³ + ....+ up to 1000 terms is equal to ________

If \(\sqrt { a+ib } \)  = x + iy, then possible value of \(\sqrt { a-ib }\) is ___________

The value of (1+i) (1+i²) (1+i³) (1+i⁴) is ____________