Question

Evaluate the radical expression, and express the result in the form $a+bi$.

$\sqrt{-49}$

Short answer

The value of radical expression is $0+7i$.

Step-by-step solution

Step 1. Concept of complex number.

A complex number is of the form $a+bi$. Where a and b are some real numbers and i is the imaginary number.

The number a is known as the real part of the complex number and b is known as imaginary part of the complex number.

Step 2. Concept of imaginary number.

The imaginary number i is defined as the square root of negative one. That is,$i=\sqrt{-1}$ or $i^2=-1$.

The properties of radicals, $\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$.

Step 3. Evaluate the radical expression.

To evaluate the given radical expression, use the concept of imaginary number and simplify further as shown below

$$\begin{gathered} \sqrt{-49}=\sqrt{-1\times 49} \\ =\sqrt{-1}\times \sqrt{49} \\ =i\times 7 \\ =7i \end{gathered}$$

Thus, the value of radical expression is $0+7i$.