Help me do this please.
Simplify the expressions using imaginary numbers.
1. √-16
2. √-49
4 sqrt -1 = 4i
7 sqrt -1 = 7i
Sure! To simplify expressions involving imaginary numbers, we need to remember the properties of the square root of a negative number.
1. √(-16):
We can simplify this expression by recognizing that the square root of -1 is denoted by the imaginary unit "i." Therefore, we can rewrite the expression as:
√(-1 * 16)
√(-1) * √(16)
i * √(16)
i * 4
4i
So, the simplified expression for √(-16) is 4i.
2. √(-49):
Similarly, we can simplify this expression by applying the same principle. We rewrite the expression as:
√(-1 * 49)
√(-1) * √(49)
i * √(49)
i * 7
So, the simplified expression for √(-49) is 7i.
In both cases, we use the fact that the square root of -1 is represented as "i" and then simplify the expression accordingly.