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In python, I have seen the following:

result = np.conjugate(result) * result

Which I presume conjugates the complex number and multiplies by the result (of the conjugate) and thus forms a real value from this.

I want to replicate this, but, I am stuck on the formula involved:

z = (-0.0106392, -0.0106392i)

Now if I conjugate these, for example, I use the following formula:

(-1 * -0.0106392)

The complex number now becomes: - z = (-0.0106392, 0.0106392i)

Now I would like to multiply these two numbers, in order to form a real value.

Could someone please give me an example? I know I could use FOIL.


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Are you wondering about the identity $(a+bi)(a-bi)=a^2+b^2$? – Lubin Jan 18 '14 at 18:53
@Lubin Hey! Just the calculation to transform the complex number into a an actual value through the use of multiplication. In the "python" code, they conjugate the complex number, and then multiply to form an actual (double) value, rather than a complex one – Phorce Jan 18 '14 at 19:02
Right. That’s how the identity arises. Throw “FOIL” away and just multiply out. – Lubin Jan 18 '14 at 21:28

What are you trying to do, exactly? Reading your comment above, I'm guessing you're trying to extract some sort of specific information about your complex number (rather than transform it into some arbitrary real number), but I'm not sure which information that is. A few possibilities:

The identity Lubin gave above, which multiplies a complex number $z=a+bi$ (where $a$ and $b$ are real numbers) by its conjugate, $\bar{z}=a-bi$, yields a real number, $a^2 + b^2$, the square root of which is equal to $z$'s distance from the origin when we plot $(a,b)$ in the plane. (This is called the absolute value or norm or modulus of $z$.)

Alternatively, if you were interested only in the real part (that is, $a$), in Python you can use the code var_name_here.real(). Note also that the imaginary part, var_name_here.imag(), is a real number. These two numbers can be viewed as the legs on a right triangle, the hypotenuse of which has length equal to the absolute value. The legs of the triangle, then, are how far over (the real part) or up (the imaginary) $z$ is from the origin.

As for an example, Lubin's comment includes one. Just remember that $i^2=-1$, and you should be able to fill in the intermediate steps.

If these possibilities don't answer you question, let me know and I'll try to update my answer.

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It kind of does, and, does make sense. For example, here: lin explains that when you conjugate a complex number, you can multiply to find a real number – Phorce Jan 18 '14 at 19:50

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