If 1, ω, ω² are the cube roots of unity then show that (1+5ω²+ω⁴) (1+5ω+ω²) (5+ω+ω⁵) = 64

Show that \(\left( \frac { i+\sqrt { 3 } }{ -i+\sqrt { 3 } } \right) ^{ 2\omega }+\left( \frac { i-\sqrt { 3 } }{ i+\sqrt { 3 } } \right) ^{ 2\omega }\) = -1

Verify that 2 arg(-1) ≠ arg(-1)²

Find all the roots \((2-2i)^{ \frac { 1 }{ 3 } }\) and also find the product of its roots.

Find the radius and centre of the circle \(z\bar { z } \)-(2+3i)z-(2-3i)\(\bar { z } \)+9 = 0 where z is a complex number.