Can help me to solve this?

1. Given that , 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 , find the possible values of z.

3. Given that z=x+yi and . If w is totally imaginary, show that .

Answers:

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

2. 3-i, 3+3i