Questions: Express √(-841) in standard form of a complex number.

Solution Steps

To express \(\sqrt{-841}\) in the standard form of a complex number, we need to recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). We can then separate the negative part and the positive part, and compute the square root of the positive part.

We start with the expression \(\sqrt{-841}\). Since the square root of a negative number involves the imaginary unit \(i\), we can rewrite the expression as: \[ \sqrt{-841} = \sqrt{841} \cdot \sqrt{-1} = \sqrt{841} \cdot i \]

Next, we calculate \(\sqrt{841}\): \[ \sqrt{841} = 29 \]

Now, we can combine the results to express \(\sqrt{-841}\) in standard form: \[ \sqrt{-841} = 29i \]

Final Answer