# Conjugate?

• Sep 13th 2009, 12:14 PM
tsmith
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?
• Sep 13th 2009, 12:21 PM
e^(i*pi)
Quote:

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 $\displaystyle i\sqrt{15}$
• Sep 13th 2009, 12:22 PM
skeeter
Quote:

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 $\displaystyle a-bi$

$\displaystyle \sqrt{-15} = 0 + (\sqrt{15})i$
• Sep 14th 2009, 04:50 AM
HallsofIvy
Quote:

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.