Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.
Multiply a complex number by a pure imaginary number and write the result in standard form
Problem
Compute \((3+4i)(2i)\) by distributing \(2i\), replacing \(i^{2}\) with \(-1\), and arranging the result in standard complex form.
Big Picture
What this problem is really about
Multiplying by a pure imaginary factor creates one imaginary term and one squared-imaginary term. We’ll distribute completely, replace the square of the imaginary unit with negative one, separate unlike components, and reorder the real term first.
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