Without using a calculator, express the complex number (2 + 6i)/(1-2i) in the form x + iy, where x and y are real.

1. (a)(i)Without using a calculator, express the complex number (2 + 6i)/(1-2i) in the form x + iy, where x and y are real.[2]
2. (a)(ii)Hence, without using a calculator, express (2 + 6i)/(1-2i) in the form r(cos θ + i sin θ), where r > 0 and -π < θ ≤ π, giving the exact values of r and θ.[3]
3. (b)On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying both the inequalities |z – 3i| ≤ 1 and Re z ≤ 0, where Re z denotes the real part of z. Find the greatest value of arg z for points in this region, giving your answer in radians correct to 2 decimal places.[5]