Question

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Answer 1

Well the first step you might do, is write out a complex number with 2 as a real part, and -4 as an imaginary part. Do you know what that means/how to do that?

Answer 2

So in general, you can write an imaginary number as \(a+bi\) where \(a\) and \(b\) are any real number (like 1, 5, 5.6, or even \(\pi\)). When people say "the real part" of a complex number, they mean the number \(a\). When people say "the imaginary part" of a complex number, they mean the number \(b\).

Answer 3

So a complex number that has real part 3, and imaginary part -7, would look like\[3-7i.\]

Answer 4

Using that as an example, what would the complex number look like with real part 2, and imaginary part -4?

Answer 5

Hold on though, we haven't found the conjugate yet.

Answer 6

Finding the conjugate of complex numbers is deceptively easy. Let's go back to the general case where our complex number is just \(a+bi\). Then the complex conjugate is just \(a-bi\). All you do is switch the sign of the imaginary part. So with the example of \(3-7i\). The complex conjugate would be \(3+7i\).

So for \(2-4i\), the complex conjugate would be....?

Answer 7

Perfect.

Answer 8

You're welcome.