Which of the following re-expresses the negative square root √-40 as a complex number in the standard form a + bi?
The negative square root of -40 can be written as √(-40) or √(40) * √(-1). Since the square root of a negative number is not a real number, it needs to be expressed in terms of "i", the imaginary unit.
The square root of 40, √(40), can be simplified as 2√10. Therefore, the negative square root of -40 can be expressed as 2√10 * √(-1).
The standard form of a complex number is a + bi, where "a" represents the real part and "b" represents the imaginary part.
In this case, the real part is 0 (2√10 multiplied by 0 is 0), and the imaginary part is 2√10. So the re-expression of the negative square root of -40 as a complex number in the standard form is:
0 + 2√10i
To re-express the negative square root √(-40) as a complex number in the standard form a + bi, we can follow the steps below:
Step 1: Simplify the expression inside the square root: √(-40)
Since the square root of a negative number is not a real number, we can express it as the square root of its absolute value multiplied by the imaginary unit "i": √(-40) = √(40) * i
Step 2: Simplify the expression further by finding the exact value of √(40):
√(40) = √(4 * 10) = √(4) * √(10) = 2 * √(10)
So, we can rewrite the expression as: √(-40) = 2√(10) * i
Therefore, the complex number in the standard form a + bi for the negative square root √(-40) is: 0 + 2√(10)i.
To re-express the negative square root √-40 as a complex number in the standard form a + bi, we need to first determine the value of the square root and then rewrite it in the form a + bi.
Let's break it down step by step:
Step 1: Determine the value of the square root of -40
The square root of -40 can be written as √(-1 * 40). Since the square root of a negative number is not a real number, we need to introduce the imaginary unit "i" to represent the square root of -1.
Step 2: Simplify the square root expression
√(-1 * 40) can be written as √(-1) * √(40). Since the square root of -1 is denoted as "i", we have √(-1) = i. So the expression becomes i * √(40).
Step 3: Simplify the square root of 40
√(40) can be further simplified as √(4 * 10), which is equal to √(4) * √(10). The square root of 4 is 2, so we get 2 * √(10).
Step 4: Rewrite the expression using the standard form a + bi
Now, combining the results from steps 2 and 3, we have i * √(40) = i * (2 * √(10)). Using the standard form a + bi, we can rewrite the expression as 0 + (2i * √(10)).
Therefore, the re-expression of the negative square root √-40 as a complex number in the standard form a + bi is 0 + (2i * √(10)).