# Thread: find the product and its conjugate-complex numbers

1. ## find the product and its conjugate-complex numbers

Can someone explain how I would solve this?

Find the product of the number and its conjugate.

square root of negative 15.

2. The product of a complex number and its conjugate is equal to the square of the modulus of the complex number.

Here,
complex number is $\displaystyle \sqrt{-15}$ or $\displaystyle i\sqrt{15}$
What is the modulus of this number?
What is conjugate of this number?

3. Originally Posted by kikitaiszcraQk
Find the product of the number and its conjugate.
$\displaystyle \left( {a + bi} \right)\overline {\left( {a + bi} \right)} = \left( {a + bi} \right)\left( {a - bi} \right) = \left( a \right)^2 - \left( {bi} \right)^2 = a^2 + b^2$

4. I don't understand how you can get "a" and "bi" from a negative square root.

5. Originally Posted by malaygoel
The product of a complex number and its conjugate is equal to the square of the modulus of the complex number.

Here,
complex number is $\displaystyle \sqrt{-15}$ or $\displaystyle i\sqrt{15}$
What is the modulus of this number?
What is conjugate of this number?
The modulus of this number would be 15 so the product is 15^2=225?

6. Originally Posted by kikitaiszcraQk
The modulus of this number would be 15 so the product is 15^2=225?
correct ...

$\displaystyle (0 + i\sqrt{15})(0 - i\sqrt{15}) = -i^2(\sqrt{15})^2 = -(-1)(15) = 15$

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### conjugate of 3-root7

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