If α and β are complex cube roots of unity, then α⁴+β⁴+α^-1β^-1=

The straight line joining the points in Argand diagram given by 0+0i and 7+7i has equation

(2+ω²+ω⁴)⁵

If (cos 3α + i sin 3α) (cos 5β+i sin 5β)=cos θ+i sin θ then θ is

(1-ω)(1-ω²) (1-ω⁴) (1-ω⁵)(1-ω⁷) )(1-ω⁸)=

If (a₁+ib₁)(a₂+ib₂)……(a_n+ib_n)=A+iB,then (a₁²+b₁²) (a₂²+b₂²)……. (a_n²+b_n²) =

The amplitude of 1+cos θ+ i sin θ is

If 3/(2+ cos θ+ i sin θ)= x+iy then (x-1)(x-3)=

Express 4+3i/(2+3i)(4-3i) in the form of x+iy

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