Question

How do you write the following quotient in standard form `(6-7i)/i`?

Answer 1

I found: `-7-6i`

Explanation:

You need to get rid of the `i` at the denominator first. To do that you can multiply and divide by the complex conjugate of the denominator;
given a complex number in the form `a+ib` the complex conjugate will be `a-ib` (change the sigh of the imaginary part). In your case you have `0+i` and the complex conjugate will be `0-i`.
So we have:
`(6-7i)/(0+i)*(0-i)/(0-i)=`
multiplying and remembering that `i^2=-1` we get:
`(-6i+7i^2)/(-i^2)=(-7-6i)/1=-7-6i` in standard form.