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Math Help - number theory

  1. #1
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    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 .
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  2. #2
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    Complex numbers

    Hi-

    Quote Originally Posted by mathaddict View Post
    (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?

    Grandad
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