Which of the following re-expresses the negative square root √-40 as a complex number in the standard form a + bi?
2√10
2i√10
4i√10
2√10i
The re-expression of the negative square root √-40 as a complex number in standard form is 2i√10.
To re-express the negative square root √-40 as a complex number in the standard form a + bi, we need to rewrite it using the imaginary unit i. Here's how you can do it step-by-step:
1. Start with √-40.
2. Rewrite -40 as -1 × 40: √(-1 × 40).
3. Split the square root: √(-1) × √(40).
4. Simplify the square root of -1: i × √(40).
5. Simplify the square root of 40: i × 2√10.
6. Rearrange the terms: 2√10i.
Therefore, the re-expression of the negative square root √-40 as a complex number in the standard form a + bi is 2√10i.
To re-express the negative square root √-40 as a complex number in the standard form a + bi, we need to first simplify the square root of -40.
The square root of a negative number is not a real number, but it can be expressed as a complex number using the imaginary unit, denoted by 'i', where i^2 = -1.
Now, let's calculate the square root of -40:
√-40 = √(40 * -1) = √40 * √-1
The square root of 40 (√40) can be simplified as 2√10, so we have:
√-40 = 2√10 * √-1
To express this in the standard form a + bi, we can write it as:
2√10 * i
Therefore, the correct re-expression of the negative square root √-40 as a complex number in the standard form a + bi is 2√10i.