Find the circle roots of -27.

Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

If the complex number 2 + i and 1-2i are equidistant from x + iy then show that x+3y = 0.

Find the locus of z if |3z - 5| = 3 |z + 1| where z = x + iy.

If \(\frac { (a+i)^{ 2 } }{ 2a-i } \) = p + iq, show that p²+q² = \(\frac { ({ a }^{ 2 }+i)^{ 2 } }{ 4a^{ 2 }+1 } \).