Exrpess each number in terms of i

a. root-21
b. -root-59
c. -root-9
d. root-28

For a:

root(-21) = root( (21)*(-1) )
= root(21) * root(-1)
= root(21) * i

That should get you started

a.

sqrt(-21)
=sqrt(21*(-1))
=sqrt(21)*sqrt(-1)
=±sqrt(21) i

c.
-sqrt(-9)
=-sqrt(9*(-1))
=∓sqrt(9)*sqrt(-1)
=∓3i

Try problems a and d along the same lines. Post your results if you need confirmation.

To express each number in terms of i, we need to simplify the square roots. Recall that the imaginary unit i is defined as i = sqrt(-1).

a. √21: Since there is no perfect square factor that can be factored out from 21, we can write sqrt(21) as sqrt(21) * 1. To express it in terms of i, we can rewrite it as sqrt(21) * sqrt(-1) = sqrt(21) * i. Therefore, √21 can be expressed as √21 i.

b. -√59: Similar to the previous example, there is no perfect square factor that can be factored out from 59. Thus, we can write -√59 as -√59 * 1. To express it in terms of i, we rewrite it as -√59 * sqrt(-1) = -√59 * i. Therefore, -√59 can be expressed as -√59 i.

c. -√9: The square root of 9 is a perfect square, which is 3. Therefore, -√9 can be simplified as -3. So, -√9 can be expressed simply as -3.

d. √28: Similar to part a, we need to factor out the perfect square factor from 28. The largest perfect square that divides evenly into 28 is 4 (2^2 = 4). So, we can rewrite √28 as √(4 * 7). Simplifying further, √4 * √7 becomes 2√7. Therefore, √28 can be expressed as 2√7.

In summary:
a. √21 can be expressed as √21 i.
b. -√59 can be expressed as -√59 i.
c. -√9 can be expressed as -3.
d. √28 can be expressed as 2√7.