Problem 7 of 7
Factor sum of squares expression 9k^2+100 over complex numbers.
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use a^2+b^2=(a+bi)(a-bi).
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Expression must be a sum of two squares or square plus positive constant.
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Solution
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1. Recognize a^2+b^2 as a^2-(bi)^2.
2. Write conjugate factors a+bi and a-bi.
3. Check by multiplying conjugates.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Saying sum of squares is unfactorable without specifying over the reals.