Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.
Multiply two complex numbers written as binomials and express the product in standard form
Problem
Expand \((2+3i)(4+i)\) using distribution, replace \(i^{2}\) with \(-1\), combine like terms, and write standard complex form.
Big Picture
What this problem is really about
Complex-binomial multiplication follows ordinary distribution, with one crucial reduction afterward. We’ll write all four products, replace the squared imaginary unit by negative one, combine real terms and imaginary terms separately, and present the standard form.
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