1. ## Conjugate?

Find the product of sqrt (-15) and its conjugate.

Ok, so I am not sure how to do this with a square root involved. Any tips?

2. Originally Posted by tsmith
Find the product of sqrt (-15) and its conjugate.

Ok, so I am not sure how to do this with a square root involved. Any tips?
$\displaystyle \sqrt{-15} = \sqrt{-1}\, \sqrt{15} = i\sqrt{15}$

In this case the conjugate will also be $\displaystyle i\sqrt{15}$

3. Originally Posted by tsmith
Find the product of sqrt (-15) and its conjugate.

Ok, so I am not sure how to do this with a square root involved. Any tips?
the conjugate of $\displaystyle a+bi$ is $\displaystyle a-bi$

$\displaystyle \sqrt{-15} = 0 + (\sqrt{15})i$

4. Originally Posted by e^(i*pi)
$\displaystyle \sqrt{-15} = \sqrt{-1}\, \sqrt{15} = i\sqrt{15}$

In this case the conjugate will also be $\displaystyle i\sqrt{15}$
That must be a typo. The conjugate of $\displaystyle i\sqrt{15}$ is $\displaystyle -i\sqrt{15}$, of course. Generally speaking a product of conjugates, (a+bi)(a-bi)= $\displaystyle a^2+ b^2$ is the square of the "modulus" of the number. Since $\displaystyle |i\sqrt{15}|= |i||\sqrt{15}|= \sqrt{15}$, that product is 15.