Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.
Simplify a complex-number expression with products or powers and write the result in standard form
Problem
Evaluate \((2+i)(3-4i)+5i\) by multiplying first, simplifying \(i^{2}\), and then combining the added imaginary term. Write standard form.
Big Picture
What this problem is really about
Order of operations keeps the complex product together before the separate term is combined. We’ll expand the factors, carry the added imaginary term forward, reduce the squared imaginary unit with its sign, combine both component groups, and interpret a zero imaginary coefficient.
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