Understand i as a number with i^2=-1 and represent complex numbers as a+bi.
Identify separate real and imaginary numeric parts
Problem
Match \(z=4+7i\) term by term to \(z=a+\text{bi}\). State the real coefficient \(a\) and the real coefficient \(b\), excluding the factor \(i\) from \(b\).
Big Picture
What this problem is really about
In standard form, the real part is the term without the imaginary unit and the imaginary coordinate is the real coefficient multiplying it. We’ll align the expression with a plus b times i, extract both coefficients without absorbing i into b, and reconstruct the number as a check.
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