Understand i as a number with i^2=-1 and represent complex numbers as a+bi.
Rewrite square roots of negative numbers in terms of i
Problem
Rewrite the principal square root \(\sqrt{-25}\) as \(\sqrt{25}\cdot~\sqrt{-1}\), substitute \(i\) for \(\sqrt{-1}\), and simplify.
Big Picture
What this problem is really about
A negative radicand can be separated into a positive magnitude and the defining factor for the imaginary unit. We’ll factor out negative one, evaluate the ordinary principal square root, replace the remaining square root with the imaginary unit, and square the result to verify the radicand.
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