Simplify the following number by using the imaginary number i.
√-63 = ?
To simplify the square root of -63 using the imaginary unit i, we can rewrite it as the product of the square root of a positive number and i.
First, let's factor -63 into its prime factors: -63 = -7 * 9.
Now, we can rewrite the square root of -63 as the square root of -7 times the square root of 9: √(-63) = √-7 * √9.
The square root of 9 is a positive number since 9 is a perfect square, so we can simplify the expression further: √(-63) = √-7 * 3.
The square root of -7 does not have a real number solution, so it is represented by the imaginary unit i: √-7 = i√7.
Therefore, the final simplified expression is: √-63 = i√7 * 3.