Understand i as a number with i^2=-1 and represent complex numbers as a+bi.
Classify a complex number as real, pure imaginary, or complex non-real
Problem
Write \(7\) as \(7+0i\). Using the mutually exclusive categories real, pure imaginary, and complex with \(\text{both}~\text{parts}~\text{nonzero}\), classify the number and justify the category from its coefficients.
Big Picture
What this problem is really about
Classification becomes unambiguous after both coefficients are exposed in standard form. We’ll write the number with an explicit zero imaginary coefficient, compare the coefficient pattern with the mutually exclusive category rules, and confirm the classification through its axis location on the complex plane.
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