Questions: Write the number as a product of a real number and i. Simplify all radical expressions. sqrt(-13) sqrt(-13)= (Simplify your answer. Type your answer in the form a+bi. Type an exact answer, using radical expressions.)

Solution Steps

To express \(\sqrt{-13}\) as a product of a real number and \(i\), we recognize that the square root of a negative number can be expressed in terms of \(i\), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-13}\) can be rewritten as \(\sqrt{13} \cdot i\).

We start with the expression \(\sqrt{-13}\). Since this is a square root of a negative number, we can express it in terms of \(i\), where \(i = \sqrt{-1}\).

Using the property of square roots, we can rewrite \(\sqrt{-13}\) as: \[ \sqrt{-13} = \sqrt{13} \cdot i \]

From the calculation, we find that: \[ \sqrt{13} \approx 3.6056 \] Thus, we can express \(\sqrt{-13}\) as: \[ \sqrt{-13} = 0 + 3.6056i \]

Final Answer