Question

How do I find the complex conjugate of `12/(5i)`?

Answer 1

The conjugate is `(12i)/5`

Explanation:

To find a conjugate of a complex number we first have to convert it to a form `a+bi`. To do this here we can multiply both numerator and denominator by `i`

`z=12/(5i)=(12i)/(5i^2)=(12i)/(-5)=-(12i)/5`

Now to calculate the conjugate we just have to change sign of the imaginary part:

`barz=(12i)/5`

Answer 2

In `a + bi` form, this starts off as:

`0 + 12/(5i)`

Note that `[12/(5i) = 12/5*1/i] != [(12i)/5 = 12/5 i]`)

`12/(5i) * (i/i) = (12i)/(5i^2) = (12i)/(-5)`

We currently have:

`a + bi = 0 + (12i)/(-5)`

The conjugate is `a - bi`, thus we get:

`a - bi = 0 - (12i)/(-5)`

`= (12i)/(5) = color(blue)(12/5 i)`