1. ## number theory

(1) Given that $(1+5i)p-2q=3+7i$ , 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 comjugate z* satisfy the equation zz*+2zi = 12 + 6i , find the possible values of z .

2. ## Complex numbers

Hi-

(1) Given that $(1+5i)p-2q=3+7i$ , 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 comjugate z* satisfy the equation zz*+2zi = 12 + 6i , find the possible values of z .
In (1), let p = a + ib, where a and b are real. Then q = a - ib.

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?