Conjugate?

**tsmith** · September 13th 2009, 12:14 PM

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?

**e^(i*pi)** · September 13th 2009, 12:21 PM

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 $i\sqrt{15}$

**skeeter** · September 13th 2009, 12:22 PM

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 $a-bi$

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

**HallsofIvy** · September 14th 2009, 04:50 AM

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.

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