Solution: Given x = a+b, y = aα +bβ and z = aβ+bα α,β are cube roots of unity. So α = ω, β = ω2 xyz = (a+b)(aα +bβ)( aβ+bα) =... View Article
Solution: Given z2+az+b = 0 Sum of roots, z1+z2 = -a Product of roots , z1z2 = b z2 = z1eiπ/3 z2 = z1( cos π/3 + i sin π/3) = z1(½ +... View Article
Solution: Given complex number = -2√3-2i Let r cos θ = -2√3 r cos θ = -2 Squaring and adding r2(cos2 θ+ sin2 θ) = (-2√3)2+22 r2 = 16 r... View Article
Solution: Since i = eiπ/2 iz = zeiπ/2 Vector iz is obtained by rotating z in anticlockwise direction through 900. |iz| = |i ||z| = 1|z|... View Article
Solution: Given (1+2i)/(2+i) = r (cos θ+i sin θ) (1+2i)(2-i)/(2+i)(2-i) = r (cos θ+i sin θ) (2+4i-i+2)/(4+1) = r (cos θ+i sin θ) (4+3i)/5 =... View Article