Problem 73 of 7
Determine whether polynomial identity (z+w)^2=z^2+2zw+w^2 remains true for complex numbers.
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substitute complex values or use algebraic proof.
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Identity must be testable by algebraic expansion or a counterexample.
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Solution
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1. Expand both sides or substitute a complex value.
2. Use i^2=-1 where needed.
3. Compare the simplified expressions.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Assuming real identities fail only because numbers are complex.