Questions: Express √(-144) - √(-25) as a complex number (in terms of i ): √(-144) - √(-25) =

Solution Steps

To express \(\sqrt{-144} - \sqrt{-25}\) as a complex number, we need to recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-144}\) can be rewritten as \(\sqrt{144} \cdot i\) and \(\sqrt{-25}\) as \(\sqrt{25} \cdot i\). Calculate the square roots of the positive numbers and then multiply by \(i\).

To express \(\sqrt{-144} - \sqrt{-25}\) as a complex number, we first recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\).

Calculate the square roots of the positive counterparts of the negative numbers:

• \(\sqrt{-144} = \sqrt{144} \cdot i = 12i\)
• \(\sqrt{-25} = \sqrt{25} \cdot i = 5i\)

Subtract the two complex numbers: \[ \sqrt{-144} - \sqrt{-25} = 12i - 5i = 7i \]

Final Answer