Which of the following is a simplification of $\sqrt{-169}$?
A. $-13$
B. $-13 i$
C. $13$
D. $13 i$
Answer (1)
Rewrite − 169 as 169 ⋅ − 1 .
Use the property a ⋅ b = a ⋅ b to rewrite the expression as 169 ⋅ − 1 .
Simplify 169 to 13 and − 1 to i .
The simplified expression is 13 i .
Explanation
Understanding the problem We are asked to simplify the square root of -169. We need to remember that − 1 = i .
Rewriting the expression Rewrite − 169 as 169 ⋅ − 1 .
Applying the square root property Use the property a ⋅ b = a ⋅ b to rewrite the expression as 169 ⋅ − 1 .
Simplifying Since 169 = 13 and − 1 = i , the simplified expression is 13 i .
Examples
Complex numbers, like the one we found, are used in electrical engineering to analyze alternating current circuits. The imaginary unit 'i' helps represent the phase difference between voltage and current, which is crucial for designing efficient power systems. By understanding complex numbers, engineers can optimize circuit performance and ensure stable operation.
