Can you conjugate this verb?

And that's the complex conjugate.

Or when you take the conjugate.

And I want to emphasize, this right here is the conjugate seven plus five, is the conjugate of seven minus five i.

So the conjugate of ztwo is c minus d i.

And the sign for conjugate is that line over the top.

Let's multiply the numerator and the denominator by the conjugate of this.

So this was c plud d i, so this is its conjugate.

So that right there is the complex conjugate of seven minus five i.

But you would have also had some of the conjugate weak base left.

Because the conjugate is the tool we're going to use to divide this.

We're asked to find the conjugate of the complex number seven minus five i.

The conjugate of c plus d i is equal to c minus d i.

So the conjugate of the denominator is going to be c minus d i.

So let's multiply the numerator and denominator of this expression by the conjugate of the denominator.

We multiply it times the conjugate of the denominator. two minus threei over over itself, right?

But seven minus five i is also the conjugate of seven plus five i, for obvious reasons.

So we know when we multiply an imaginary number times its conjugate, we get a real number.

Or you could say, the conjugate of c minus d i is equal to c plus d i.

And what you're going to find in this video is finding the conjugate of a complex number is shockingly easy.

Now you're probably saying ok, fairly straightforward to find a conjugate of a complex number, but what is it good for?

And notice, we're just switching the direction in the imaginary along the imaginary axis, when we take the conjugate of something.

I've been calling theta the parameters of the model are mostly continued to use that terminology to conjugate to the parameters, but the neural networks.

you'll see z is the variable people often use for complex numbers if z is seven minus five i, then they'll say complex conjugate of z,

If you have seven minus five i, and you put a line over it like that, that means you want the conjugate of seven minus five i.

If we multiply both the numerator and the denominator of this expression by the complex conjugate of the denominator, then we will have a real number in the denominator.

It has the same real parts, so the conjugate of this is going to have the exact same real part, but its imaginary part is going to have the opposite sign.

And the simplest reason, or the most basic place where this is useful is when you multiply any imaginary, any complex number times its conjugate, you're going to get a real number.

And, in general, this number if we call this well, in our example this was ztwo, so if we say that ztwo equals c plus d i, the quantity c minus d i is called its conjugate.