Question 1106748
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1.  Evaluate the modulus  of the left side for |z| <= {{{sqrt(2)}}}:


       |z^8 + (1+i)*z^3 + 2*z^2| <= (apply the "triangle inequality" to the modulus of the sum of complex numbers) <=

    <= |z^8| + |(1+i)|*|z*3| + 2*|z^2| <= {{{(sqrt(2))^8}}} + {{{sqrt(2)*(sqrt(2))^3}}} + {{{2*(sqrt(2))^2}}} = 16 + 4 + 4 = 24.



2.  Evaluate the modulus of the right side:

    |10 + 24i| = {{{sqrt(10^2 + 24^2)}}} > 24.



3.  Comparing n.1  with n.2,  you may conclude that the equation  <U>HAS NO solutions</U>  in the given domain.
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