(Solved): (4) (a) Compute \( \left|(6+8 i)^{9}\right| \). (b) By writing \( z=a+b i, w=c+d i \) prove that \ ...

(4) (a) Compute \( \left|(6+8 i)^{9}\right| \). (b) By writing \( z=a+b i, w=c+d i \) prove that \( \overline{z \cdot w}=\bar{z} \cdot \bar{w} \). (c) Find all complex solutions of the following equation: \( \overline{z-i}=6-2 z \). \( [3+4+3=10 \) marks