Express in terms of i.
2 divided by sqrt.,-36
2/√-36
= 2/6i or
2/6i * i/i
= 2i/-6
= -i/3
so 2/6i or -i/3
To express the expression 2 divided by the square root of -36 in terms of i (the imaginary unit), we need to simplify the expression first.
First, let's focus on the square root of -36. The square root of a negative number is not a real number, but rather an imaginary number. In this case, the square root of -36 can be written as 6i, since the square root of 36 is 6 and the square root of -1 is i.
Now we have 2 divided by 6i. To divide by a complex number, we multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of 6i is -6i.
Multiplying the numerator and denominator by -6i, we get:
(2 * -6i) / (6i * -6i)
Simplifying further:
-12i / (36i^2)
Since i^2 is equal to -1:
-12i / (36 * -1)
Finally, simplifying the expression:
-12i / -36
Since -12 divided by -36 is 1/3, the expression can be written as:
1/3i
Therefore, 2 divided by the square root of -36 expressed in terms of i is 1/3i.