Question

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Explanation:

Step1: Simplify the square root of -144

We know that \(\sqrt{-144}=\sqrt{-1\times144}=\sqrt{-1\times12^{2}}\), so the first blank is \(-1\).

Step2: Use the imaginary unit \(i\)

Recall that \(i = \sqrt{-1}\), so \(\sqrt{-1\times12^{2}}=\sqrt{-1}\times\sqrt{12^{2}} = i\times\sqrt{12^{2}}\), so the second blank is \(i\).

Step3: Simplify \(\sqrt{12^{2}}\)

Since \(\sqrt{12^{2}} = 12\), then \(i\times\sqrt{12^{2}}=i\times12 = 12i\), so the third blank is \(12i\).

Answer:

First blank: \(-1\)
Second blank: \(i\)
Third blank: \(12i\)