Put these expressions in place of p and q in the equation.
Expand the brackets, separate out the reals and imaginaries and put the real part equal to 3 and the imaginary part equal to 7.
This will give you a pair of simultaneous equations in a and b, which you can then solve.
In (2), let z = a + ib, where a and b are real. Then z* = a - ib.
Substitute these into the LHS, expand and then compare reals and imaginaries. Again, this gives two equations for a and b, which you can solve.
Is that enough to get you going?