Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.
Multiply a complex number by a real number and write the result in standard form
Problem
Compute \(2(3+4i)\) by distributing the real scalar \(2\) to \(\text{both}~\text{the}~\text{real}~\text{and}~\text{imaginary}~\text{terms}\). Write the product in standard form.
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What this problem is really about
A real scalar multiplies both coordinates of a complex number. We’ll distribute the factor to the real and imaginary terms, scale each coefficient, preserve the imaginary unit on its component, and assemble the product in standard form.
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