SOLUTION: If z= x+iy , and z³ × conj(z) + conj(z)³ × z = 350 , then (x, y)=.....

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Question 1205326: If z= x+iy , and z³ × conj(z) + conj(z)³ × z = 350 , then (x, y)=.....
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If z=+x%2Biy , conj%28z%29=+x-iy

and if z%5E3+%2A+conj%28z%29+%2B+conj%28z%29%5E3%2A+z+=+350 , then

%28x%2Biy%29%5E3+%2A+%28x-iy%29+%2B+%28x-iy%29%5E3%2A+%28x%2Biy%29+=+350
%28x%2Biy%29%5E2+%2A+%28x%5E2%2By%5E2%29+%2B%28x-iy%29%5E2%2A+%28x%5E2%2By%5E2%29+=+350
%28%28x%2Biy%29%5E2+%2B%28x-iy%29%5E2%29%2A+%28x%5E2%2By%5E2%29=350
2%28x+-+y%29%28x+%2B+y%29%28x%5E2+%2B+y%5E2%29=+350
%28x+-+y%29%28x+%2B+y%29%28x%5E2+%2B+y%5E2%29=+175
%28x%5E2+-+y%5E2%29+%28x%5E2+%2B+y%5E2%29=+175
x%5E4+-+y%5E4+=+175