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 .
1. p=2-i, q=2+i
2. 3-i, 3+3i
Going a bit backwards here:
If , then :
Now equate the real and imaginary coefficients:
So the answers, in the form of a + bi, are
3 + 3i and
3 - i.