Can help me to solve this?

1. Given that $\displaystyle (1+5i)p-2q=3+7i$, find the values of p and q when p and q are respectively a complex number and its conjugate.

2. Given that the complex number z and its conjugate z* satisfy the equation $\displaystyle zz*+2zi=12+6i$, find the possible values of z.

3. Given that z=x+yi and $\displaystyle w= \frac {z+8i}{z-6}$. If w is totally imaginary, show that $\displaystyle x^2+y^2+2x-48=0$.

Answers:

1. p=2-i, q=2+i

2. 3-i, 3+3i