express in terms of i
- sqrt -496
- √-496
=-√16 √-31
= -4√31 i
To express √(-496) in terms of the imaginary unit "i", we'll start by simplifying the square root of the absolute value of -496 and then introduce "i" to express the result in terms of complex numbers.
Step 1: Determine the absolute value of -496.
The absolute value of -496 is 496 since the absolute value removes the negative sign.
Step 2: Simplify the square root of 496.
We can write √496 as √(16 * 31). Notice that 16 is a perfect square, so we can take it out of the square root sign. Also, we can't simplify the square root of 31 further since it is not a perfect square.
√(16 * 31) = √16 * √31 = 4√31
Step 3: Introduce "i" to express the result.
Since √(-1) is represented as "i", we can rewrite 4√31 as 4√(31 * -1) and then simplify it further:
4√(31 * -1) = 4√31 * √(-1) = 4√31 * i
Therefore, √(-496) can be expressed in terms of "i" as 4√31 * i.