Question

What is the complex conjugate of `3i+4`?

Answer 1

If `z=4+3i` then `bar z = 4-3i`

A conjugate of a complex number is a number with the same real part and an oposite imaginary part.

In the example :
`re(z) = 4` and `im(z)=3i`
So the conjugate has:
`re(bar z) = 4` and `im(bar z)=-3i`
So `bar z = 4-3i`

Note to a question : It is more usual to start a complex number with the real part so it would rather be written as `4+3i` not as `3i+4`

Answer 2

`4-3i`

Explanation:

To find a complex conjugate, simply change the sign of the imaginary part (the part with the `i`). This means that it either goes from positive to negative or from negative to positive.

As a general rule, the complex conjugate of `a+bi` is `a-bi`.

Notice that `3i+4=4+3i`, which is the generally accepted order for writing terms in a complex number.

Therefore, the complex conjugate of `4+3i` is `4-3i`.