Question 983314
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{{{(x+yi)(x+yi)=3+4i}}}


{{{x^2+2xyi+y^2*i^2}}}


{{{x^2+y^2*i^2+2xyi}}}


{{{x^2+(-1)y^2+2xyi}}}


{{{x^2-y^2+2xyi}}} compare corresponding parts to {{{3+4i}}}.


{{{system(x^2-y^2=3,2xy=4)}}}
Find either variable or the other using the second equation and substitute into the first equation:
{{{y=2/x}}};
{{{x^2-(2/x)^2=3}}}
{{{x^4-2=3x^2}}}
{{{x^4-3x^2-2=0}}}
---not factorable---
{{{x^2=(3+- sqrt(9+4*2))/2}}}
{{{x^2=(3+- sqrt(17))/2}}}
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{{{highlight(x=0+- sqrt((3+- sqrt(17))/2))}}}-----this is four different values.


You want to be sure that any y value you find corresponds to the proper x value.  Go back to {{{y=2/x}}}, and find the y which corresponds with any individual chosen x.