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Math Help - complex problem

  1. #1
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    complex problem

    if mod(z1)=1 mod(z2)=2 mod(z3)=3 and mod(9z1z2+4z1z3+z2z3)=12 find the value of mod(z1+z2+z3)

    i know mod(z1+z2+z3)<=mod(z1)+mod(z2)+mod(z3) but how to do this
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  2. #2
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    Quote Originally Posted by prasum View Post
    if mod(z1)=1 mod(z2)=2 mod(z3)=3 and mod(9z1z2+4z1z3+z2z3)=12 find the value of mod(z1+z2+z3)

    i know mod(z1+z2+z3)<=mod(z1)+mod(z2)+mod(z3) but how to do this
    Use the fact that |z|^2 = z\overline{z}. So z_1\overline{z_1} = 1, z_2\overline{z_2} = 4, z_3\overline{z_3} = 9, and (9z_1z_2 + 4z_1z_3 + z_2z_3)(9\overline{z_1z_2} + 4\overline{z_1z_3} + \overline{z_2z_3}) = 144. Multiply out that last one to get an expression for z_1\overline{z_2} + z_1\overline{z_3} + z_2\overline{z_3}. That will enable you to find (z_1 + z_2 + z_3)(\overline{z_1} + \overline{z_2} + \overline{z_3}).
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