If the point z₁ = 1 + i, where $$i = \sqrt { - 1} $$ is the reflection of a point z₂ = x + iy in the line $$i\overline z - iz = 5$$, then the point z₂ is

$$z\overline z + (3 - i)z + (3 + i)\overline z + 1 = 0$$ represents a circle with

What is $$\sqrt {{{1 + {\omega ^2}} \over {1 + \omega }}} $$ equal to, where $$\omega$$ is the cube root of unity?

What is $${\omega ^{100}} + {\omega ^{200}} + {\omega ^{300}}$$ equal to, where $$\omega$$ is the cube root of unity?