Simplify the following expression; express in terms of i.
(this radical is) square root of -16?
4i
i as an imaginary number)
To simplify the expression and express it in terms of i, let's break it down step by step:
1. Start with the expression: √(-16)
2. Since the square root of a negative number is not defined in the real number system, we need to introduce the imaginary unit, 'i'. The imaginary unit, i, is defined as the square root of -1.
3. Rewrite the expression as: √(-1 * 16)
4. Simplify the expression under the square root as: √(-1) * √(16)
5. The square root of 16 is 4, so the expression becomes: 4 * √(-1)
6. Finally, combine the simplified expression with the imaginary unit, i, to get the final answer: 4i
Therefore, the simplified expression, expressed in terms of i, is 4i.
To simplify the expression and express it in terms of "i", let's work step by step.
The square root of -16 can be rewritten as √(-1 * 16).
Now, we can take the square root of each factor separately:
√(-1) * √(16).
The square root of 16 is 4, since 4 * 4 = 16.
So we are left with √(-1) * 4.
Now, let's express the square root of -1 in terms of "i". The imaginary unit "i" is defined as √(-1).
So, √(-1) can be written as "i".
Now, we can substitute √(-1) with "i" in our expression:
i * 4.
Finally, we simplify this further by multiplying "i" with 4:
4i.
Therefore, the simplified expression in terms of "i" for the square root of -16 is 4i.