Let $a$ and $b$ be real numbers so that the roots of
\[z^2 + (10 + ai) z + (27 + bi) = 0\]are complex conjugates.  Enter the ordered pair $(a,b).$
Question:
Let $a$ and $b$ be real numbers so that the roots of
\[z^2 + (10 + ai) z + (27 + bi) = 0\]are complex conjugates.  Enter the ordered pair $(a,b).$
Answer:
Let's think step by step.

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Let $a$ and $b$ be real numbers so that the roots of
\[z^2 + (10 + ai) z + (27 + bi) = 0\]are complex conjugates.  Enter the ordered pair $(a,b).$
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