# Conjugate?

• Sep 13th 2009, 01:14 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, 01:21 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?

$\sqrt{-15} = \sqrt{-1}\, \sqrt{15} = i\sqrt{15}$

In this case the conjugate will also be $i\sqrt{15}$
• Sep 13th 2009, 01:22 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 $a+bi$ is $a-bi$

$\sqrt{-15} = 0 + (\sqrt{15})i$
• Sep 14th 2009, 05:50 AM
HallsofIvy
Quote:

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

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

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